MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

1.9Converting from Decimal to Binary and

Hexadecimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Goal

To be able to correctly convert a decimal numberinto a binary number and a hexadecimal number.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Convert 20 to a binary number.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

0 1 0 1 0 0

Place value32 16 8 4 2 1

Place value25 24 23 22 21 20

Convert 20 to a binary number.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

0 1 0 1 0 0

Place value32 16 8 4 2 1

Place value25 24 23 22 21 20

Convert 20 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

0 1 0 1 0 0

Place value32 16 8 4 2 1

Place value25 24 23 22 21 20

Convert 20 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

0 1 0 1 0 0

Place value32 16 8 4 2 1

Place value25 24 23 22 21 20

Convert 20 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

0 1 0 1 0 0

Place value32 16 8 4 2 1

Place value25 24 23 22 21 20

Convert 20 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

0 1 0 1 0 0

Place value32 16 8 4 2 1

Place value25 24 23 22 21 20

Convert 20 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

0 1 0 1 0 0

Place value32 16 8 4 2 1

Place value25 24 23 22 21 20

Convert 20 to a binary number.

20 = 0101002

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

0 1 1 0 1 0

Place value 32 16 8 4 2 1

Convert 26 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

0 1 1 0 1 0

Place value 32 16 8 4 2 1

Convert 26 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

0 1 1 0 1 0

Place value 32 16 8 4 2 1

Convert 26 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

0 1 1 0 1 0

Place value 32 16 8 4 2 1

Convert 26 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

0 1 1 0 1 0

Place value 32 16 8 4 2 1

Convert 26 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

0 1 1 0 1 0

Place value 32 16 8 4 2 1

Convert 26 to a binary number.

26 = 0110102

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

1 0 0 1 1 1

Place value 32 16 8 4 2 1

Convert 39 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

1 0 0 1 1 1

Place value 32 16 8 4 2 1

Convert 39 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

1 0 0 1 1 1

Place value 32 16 8 4 2 1

Convert 39 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

1 0 0 1 1 1

Place value 32 16 8 4 2 1

Convert 39 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

1 0 0 1 1 1

Place value 32 16 8 4 2 1

Convert 39 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

1 0 0 1 1 1

Place value 32 16 8 4 2 1

Convert 39 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

1 0 0 1 1 1

Place value 32 16 8 4 2 1

Convert 39 to a binary number.

39 = 1001112

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary Numbers

Digit(Face value)

1 1 1 1 1 1

Place value 32 16 8 4 2 1

What’s the biggest number that can berepresented by 6 bits?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary Numbers

Digit(Face value)

1 1 1 1 1 1

Place value 32 16 8 4 2 1

What’s the biggest number that can berepresented by 6 bits?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary Numbers

Digit(Face value)

1 1 1 1 1 1

Place value 32 16 8 4 2 1

What’s the biggest number that can berepresented by 6 bits?

1111112 = 63

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary Numbers

Digit(Face value)

1 1 1 1 1 1

Place value 32 16 8 4 2 1

What’s the biggest number that can berepresented by 6 bits?

1111112 = 63 = 64 - 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary Numbers

Digit(Face value)

1 1 1 1 1 1

Place value 32 16 8 4 2 1

What’s the biggest number that can berepresented by 6 bits?

1111112 = 63 = 64 - 1 = 26 - 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary Numbers

Digit(Face value)

1 1 1 1 1 1

Place value 32 16 8 4 2 1

What’s the biggest number that can berepresented by 6 bits?

1111112 = 63 = 64 - 1 = 26 - 1

Note that the exponent is equal to the

number of bits

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary Numbers

Digit(Face value)

1 1 1 1 1 1 1 1

Place value 128 64 32 16 8 4 2 1

What’s the biggest number that can berepresented by 8 bits?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary Numbers

Digit(Face value)

1 1 1 1 1 1 1 1

Place value 128 64 32 16 8 4 2 1

What’s the biggest number that can berepresented by 8 bits?

111111112 = 255

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary Numbers

Digit(Face value)

1 1 1 1 1 1 1 1

Place value 128 64 32 16 8 4 2 1

What’s the biggest number that can berepresented by 8 bits?

111111112 = 255 = 256 - 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary Numbers

Digit(Face value)

1 1 1 1 1 1 1 1

Place value 128 64 32 16 8 4 2 1

What’s the biggest number that can berepresented by 8 bits?

111111112 = 255 = 256 - 1 = 28 - 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary Numbers

What’s the biggest number that can berepresented by 12 bits?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary Numbers

What’s the biggest number that can berepresented by 12 bits?

1111111111112 = 212 - 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary Numbers

What’s the biggest number that can berepresented by 12 bits?

1111111111112 = 212 - 1 = 4095

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

1 0 0 1 1 1

Place value 32 16 8 4 2 1

Convert 39 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

1 0 0 1 1 1

Place value 32 16 8 4 2 1

Convert 39 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

1 0 0 1 1 1

Place value 32 16 8 4 2 1

Convert 39 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

1 0 0 1 1 1

Place value 32 16 8 4 2 1

Convert 39 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

1 0 0 1 1 1

Place value 32 16 8 4 2 1

Convert 39 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

1 0 0 1 1 1

Place value 32 16 8 4 2 1

Convert 39 to a binary number.

Which bits need to be turned on?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

1 0 0 1 1 1

Place value 32 16 8 4 2 1

Convert 39 to a binary number.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Digit(Face value)

1 0 0 1 1 1

Place value 32 16 8 4 2 1

Convert 39 to a binary number.

39 = 1001112

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

Convert 39 to a binary number.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 0

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 0

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

We stop dividing once the

quotient is 0

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

We write down the

remainders starting with the last one

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

39 =

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

We write down the

remainders starting with the last one

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

39 =

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

39 = 1

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

39 = 1

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

39 = 10

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

39 = 10

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

39 = 100

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

39 = 100

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

39 = 1001

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

39 = 1001

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

39 = 10011

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

39 = 10011

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

39 = 100111

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

39 = 100111

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

39 = 1001112

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 105 to a binary number.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 105 to a binary number. 105 ÷ 2 = 52 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 105 to a binary number. 105 ÷ 2 = 52 rem 152 ÷ 2 = 26 rem 0

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 105 to a binary number. 105 ÷ 2 = 52 rem 152 ÷ 2 = 26 rem 026 ÷ 2 = 13 rem 0

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 105 to a binary number. 105 ÷ 2 = 52 rem 152 ÷ 2 = 26 rem 026 ÷ 2 = 13 rem 013 ÷ 2 = 6 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 105 to a binary number. 105 ÷ 2 = 52 rem 152 ÷ 2 = 26 rem 026 ÷ 2 = 13 rem 013 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 0

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 105 to a binary number. 105 ÷ 2 = 52 rem 152 ÷ 2 = 26 rem 026 ÷ 2 = 13 rem 013 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 03 ÷ 2 = 1 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 105 to a binary number. 105 ÷ 2 = 52 rem 152 ÷ 2 = 26 rem 026 ÷ 2 = 13 rem 013 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 03 ÷ 2 = 1 rem 11 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 105 to a binary number. 105 ÷ 2 = 52 rem 152 ÷ 2 = 26 rem 026 ÷ 2 = 13 rem 013 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 03 ÷ 2 = 1 rem 11 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 105 to a binary number. 105 ÷ 2 = 52 rem 152 ÷ 2 = 26 rem 026 ÷ 2 = 13 rem 013 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 03 ÷ 2 = 1 rem 11 ÷ 2 = 0 rem 1

quotient

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 105 to a binary number. 105 ÷ 2 = 52 rem 152 ÷ 2 = 26 rem 026 ÷ 2 = 13 rem 013 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 03 ÷ 2 = 1 rem 11 ÷ 2 = 0 rem 1

quotient remainder

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 105 to a binary number. 105 ÷ 2 = 52 rem 152 ÷ 2 = 26 rem 026 ÷ 2 = 13 rem 013 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 03 ÷ 2 = 1 rem 11 ÷ 2 = 0 rem 1

quotient remainder

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

105 = 11010012

Convert 105 to a binary number. 105 ÷ 2 = 52 rem 152 ÷ 2 = 26 rem 026 ÷ 2 = 13 rem 013 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 03 ÷ 2 = 1 rem 11 ÷ 2 = 0 rem 1

quotient remainder

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How can we modify the method we just looked at so that it will work for converting decimal numbers to hexadecimal?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How can we modify the method we just looked at so that it will work for converting decimal numbers to hexadecimal?Convert 125 to a hexadecimal number.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How can we modify the method we just looked at so that it will work for converting decimal numbers to hexadecimal?Convert 125 to a hexadecimal number.

Instead of dividing by 2, we divide by 16. Remember that hexadecimal is “base 16”.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How can we modify the method we just looked at so that it will work for converting decimal numbers to hexadecimal?Convert 125 to a hexadecimal number.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How can we modify the method we just looked at so that it will work for converting decimal numbers to hexadecimal?Convert 125 to a hexadecimal number. 125 ÷ 16 = 7 rem 13

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How can we modify the method we just looked at so that it will work for converting decimal numbers to hexadecimal?Convert 125 to a hexadecimal number. 125 ÷ 16 = 7 rem 13

7 ÷ 16 = 0 rem 7

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How can we modify the method we just looked at so that it will work for converting decimal numbers to hexadecimal?Convert 125 to a hexadecimal number. 125 ÷ 16 = 7 rem 13

7 ÷ 16 = 0 rem 7

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How can we modify the method we just looked at so that it will work for converting decimal numbers to hexadecimal?Convert 125 to a hexadecimal number. 125 ÷ 16 = 7 rem 13

7 ÷ 16 = 0 rem 7

Note that 13 = D

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How can we modify the method we just looked at so that it will work for converting decimal numbers to hexadecimal?

125 = 7D16

Convert 125 to a hexadecimal number. 125 ÷ 16 = 7 rem 137 ÷ 16 = 0 rem 7

Note that 13 = D

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 3973 to a hexadecimal number.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 3973 to a hexadecimal number. 3973 ÷ 16 = 248 rem 5

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 3973 to a hexadecimal number. 3973 ÷ 16 = 248 rem 5248 ÷ 16 = 15 rem 8

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 3973 to a hexadecimal number. 3973 ÷ 16 = 248 rem 5248 ÷ 16 = 15 rem 815 ÷ 16 = 0 rem 15

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 3973 to a hexadecimal number. 3973 ÷ 16 = 248 rem 5248 ÷ 16 = 15 rem 815 ÷ 16 = 0 rem 15

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 3973 to a hexadecimal number. 3973 ÷ 16 = 248 rem 5248 ÷ 16 = 15 rem 815 ÷ 16 = 0 rem 15

Note that 15 = F

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

3973 = F8516

Convert 3973 to a hexadecimal number. 3973 ÷ 16 = 248 rem 5248 ÷ 16 = 15 rem 815 ÷ 16 = 0 rem 15

Note that 15 = F

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

The “fractional part” is the part to the right of the point (or period).

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.7 to a binary number.

The “fractional part” is the part to the right of the point (or period).

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.7 to a binary number. 0.7 • 2 = 1.4

The “fractional part” is the part to the right of the point (or period).

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.7 to a binary number. 0.7 • 2 = 1.4

The “fractional part” is the part to the right of the point (or period).

This time we multiply instead of

dividing

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.7 to a binary number. 0.7 • 2 = 1.4

The “fractional part” is the part to the right of the point (or period).

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.8

The “fractional part” is the part to the right of the point (or period).

We use only the fractional part in the next line

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.6

The “fractional part” is the part to the right of the point (or period).

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.2

The “fractional part” is the part to the right of the point (or period).

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.4

The “fractional part” is the part to the right of the point (or period).

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.8

The “fractional part” is the part to the right of the point (or period).

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.8

The “fractional part” is the part to the right of the point (or period).

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.8

The “fractional part” is the part to the right of the point (or period).

Notice here that 0.8 has appeared again. Once that happens, we know that we have a repeating pattern.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.8

Notice here that 0.8 has appeared again. Once that happens, we know that we have a repeating pattern.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.8

Notice here that 0.8 has appeared again. Once that happens, we know that we have a repeating pattern.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.8

Notice here that 0.8 has appeared again. Once that happens, we know that we have a repeating pattern.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.8

Notice here that 0.8 has appeared again. Once that happens, we know that we have a repeating pattern.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.4

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.4

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.4

This time, instead of reading

the 0s and 1s upwards, we read them downwards

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

0.7 = .1

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.4

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

0.7 = .1

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.4

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

0.7 = .10

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.4

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

0.7 = .10

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.4

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

0.7 = .101

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.4

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

0.7 = .101

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.4

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

0.7 = .1011

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.4

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

0.7 = .1011

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.4

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

0.7 = .10110

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.4

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

0.7 = .10110

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.4

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

0.7 = .10110

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.4

We know that “0110” is a repeating pattern. So we put a bar on top of the pattern.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

0.7 = .10110

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.4

We know that “0110” is a repeating pattern. So we put a bar on top of the pattern.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

0.7 = .101102

Convert 0.7 to a binary number. 0.7 • 2 = 1.40.4 • 2 = 0.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.4

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example?

Convert 0.875 to a binary number.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example?

Convert 0.875 to a binary number. 0.875 • 2 = 1.75

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example?

Convert 0.875 to a binary number. 0.875 • 2 = 1.750.75 • 2 = 1.50

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example?

Convert 0.875 to a binary number. 0.875 • 2 = 1.750.75 • 2 = 1.50

0.5 • 2 = 1.0

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example?

Convert 0.875 to a binary number. 0.875 • 2 = 1.750.75 • 2 = 1.50

0.5 • 2 = 1.0

If the fractional part is 0, then we can stop

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example?

Convert 0.875 to a binary number. 0.875 • 2 = 1.750.75 • 2 = 1.50

0.5 • 2 = 1.0

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example?

Convert 0.875 to a binary number. 0.875 • 2 = 1.750.75 • 2 = 1.50

0.5 • 2 = 1.0

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example?

0.875 = .1112

Convert 0.875 to a binary number. 0.875 • 2 = 1.750.75 • 2 = 1.50

0.5 • 2 = 1.0

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 0.95 to a binary number.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 0.95 to a binary number. 0.95 • 2 = 1.9

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 0.95 to a binary number. 0.95 • 2 = 1.90.90 • 2 = 1.8

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 0.95 to a binary number. 0.95 • 2 = 1.90.90 • 2 = 1.80.8 • 2 = 1.6

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 0.95 to a binary number. 0.95 • 2 = 1.90.90 • 2 = 1.80.8 • 2 = 1.60.6 • 2 = 1.2

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 0.95 to a binary number. 0.95 • 2 = 1.90.90 • 2 = 1.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.4

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 0.95 to a binary number. 0.95 • 2 = 1.90.90 • 2 = 1.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.8

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 0.95 to a binary number. 0.95 • 2 = 1.90.90 • 2 = 1.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.80.8 • 2 = 1.6

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 0.95 to a binary number. 0.95 • 2 = 1.90.90 • 2 = 1.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.80.8 • 2 = 1.6

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 0.95 to a binary number. 0.95 • 2 = 1.90.90 • 2 = 1.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.8

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 0.95 to a binary number. 0.95 • 2 = 1.90.90 • 2 = 1.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.8

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 0.95 to a binary number. 0.95 • 2 = 1.90.90 • 2 = 1.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.8

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 0.95 to a binary number. 0.95 • 2 = 1.90.90 • 2 = 1.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.8

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Here’s another example:

Convert 0.95 to a binary number.

0.95 = .1111002

0.95 • 2 = 1.90.90 • 2 = 1.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.8

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How do we convert decimal numbers with a fractional part into hexadecimal?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How do we convert decimal numbers with a fractional part into hexadecimal?

Convert 0.35 to a hexadecimal number.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How do we convert decimal numbers with a fractional part into hexadecimal?

Convert 0.35 to a hexadecimal number. 0.35 • 16 = 5.6

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How do we convert decimal numbers with a fractional part into hexadecimal?

Convert 0.35 to a hexadecimal number. 0.35 • 16 = 5.60.6 • 16 = 9.6

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How do we convert decimal numbers with a fractional part into hexadecimal?

Convert 0.35 to a hexadecimal number. 0.35 • 16 = 5.60.6 • 16 = 9.60.6 • 16 = 9.6

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How do we convert decimal numbers with a fractional part into hexadecimal?

Convert 0.35 to a hexadecimal number. 0.35 • 16 = 5.60.6 • 16 = 9.6

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How do we convert decimal numbers with a fractional part into hexadecimal?

Convert 0.35 to a hexadecimal number. 0.35 • 16 = 5.60.6 • 16 = 9.6

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How do we convert decimal numbers with a fractional part into hexadecimal?

Convert 0.35 to a hexadecimal number. 0.35 • 16 = 5.60.6 • 16 = 9.6

0.35 = .5916

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 0.25 to a hexadecimal number.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 0.25 to a hexadecimal number. 0.25 • 16 = 4.0

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 0.25 to a hexadecimal number. 0.25 • 16 = 4.0

If the fractional part is 0, then we can stop

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

0.25 = .416

Convert 0.25 to a hexadecimal number. 0.25 • 16 = 4.0

If the fractional part is 0, then we can stop

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 0.24 to a hexadecimal number.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 0.24 to a hexadecimal number. 0.24 • 16 = 3.84

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 0.24 to a hexadecimal number. 0.24 • 16 = 3.840.84 • 16 = 13.44

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 0.24 to a hexadecimal number. 0.24 • 16 = 3.840.84 • 16 = 13.440.44 • 16 = 7.04

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 0.24 to a hexadecimal number. 0.24 • 16 = 3.840.84 • 16 = 13.440.44 • 16 = 7.040.04 • 16 = 0.64

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 0.24 to a hexadecimal number. 0.24 • 16 = 3.840.84 • 16 = 13.440.44 • 16 = 7.040.04 • 16 = 0.64

0.64 • 16 = 10.24

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 0.24 to a hexadecimal number. 0.24 • 16 = 3.840.84 • 16 = 13.440.44 • 16 = 7.040.04 • 16 = 0.64

0.64 • 16 = 10.240.24 • 16 = 3.84

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 0.24 to a hexadecimal number. 0.24 • 16 = 3.840.84 • 16 = 13.440.44 • 16 = 7.040.04 • 16 = 0.64

0.64 • 16 = 10.240.24 • 16 = 3.84

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 0.24 to a hexadecimal number. 0.24 • 16 = 3.840.84 • 16 = 13.440.44 • 16 = 7.040.04 • 16 = 0.64

0.64 • 16 = 10.24

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

Convert 0.24 to a hexadecimal number. 0.24 • 16 = 3.840.84 • 16 = 13.440.44 • 16 = 7.040.04 • 16 = 0.64

0.64 • 16 = 10.24

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

Here’s another example:

0.24 = .3D70A16

Convert 0.24 to a hexadecimal number. 0.24 • 16 = 3.840.84 • 16 = 13.440.44 • 16 = 7.040.04 • 16 = 0.64

0.64 • 16 = 10.24

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 39.95 to a binary number.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 39.95 to a binary number.

To perform this conversion, separate the decimal number into its two parts: 39 and .95

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

39 = 1001112

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

Let’s look at another method for converting decimal numbers to binary.

39 = 1001112

Convert 39 to a binary number. 39 ÷ 2 = 19 rem 119 ÷ 2 = 9 rem 19 ÷ 2 = 4 rem 14 ÷ 2 = 2 rem 02 ÷ 2 = 1 rem 01 ÷ 2 = 0 rem 1

We converted 39 in this slide earlier. So we know that 39 is 1001112

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.95 to a binary number. 0.95 • 2 = 1.90.90 • 2 = 1.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.80.8 • 2 = 1.6

0.95 = .1111002

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 0.95 to a binary number. 0.95 • 2 = 1.90.90 • 2 = 1.80.8 • 2 = 1.60.6 • 2 = 1.20.2 • 2 = 0.40.4 • 2 = 0.80.8 • 2 = 1.6

0.95 = .1111002

We converted 0.95 in this slide earlier. So we know that 0.95 is .1111002

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 39.95 to a binary number.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 39.95 to a binary number.

39 = 1001112

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 39.95 to a binary number.

39 = 10011120.95 = .1111002

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 39.95 to a binary number.

39 = 10011120.95 = .1111002

Therefore,

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 39.95 to a binary number.

39 = 10011120.95 = .1111002

Therefore,39.95 = 100111. 1111002

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 54.75 to a binary number.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 54.75 to a binary number.

54 ÷ 2 = 27 rem 0

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 54.75 to a binary number.

54 ÷ 2 = 27 rem 027 ÷ 2 = 13 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 54.75 to a binary number.

54 ÷ 2 = 27 rem 027 ÷ 2 = 13 rem 113 ÷ 2 = 6 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 54.75 to a binary number.

54 ÷ 2 = 27 rem 027 ÷ 2 = 13 rem 113 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 0

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 54.75 to a binary number.

54 ÷ 2 = 27 rem 027 ÷ 2 = 13 rem 113 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 03 ÷ 2 = 1 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 54.75 to a binary number.

54 ÷ 2 = 27 rem 027 ÷ 2 = 13 rem 113 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 03 ÷ 2 = 1 rem 11 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 54.75 to a binary number.

54 ÷ 2 = 27 rem 027 ÷ 2 = 13 rem 113 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 03 ÷ 2 = 1 rem 11 ÷ 2 = 0 rem 1

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 54.75 to a binary number.

54 ÷ 2 = 27 rem 027 ÷ 2 = 13 rem 113 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 03 ÷ 2 = 1 rem 11 ÷ 2 = 0 rem 1

54 = 1101102

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 54.75 to a binary number.

54 ÷ 2 = 27 rem 027 ÷ 2 = 13 rem 113 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 03 ÷ 2 = 1 rem 11 ÷ 2 = 0 rem 1

54 = 1101102

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 54.75 to a binary number.

.75 • 2 = 1.554 ÷ 2 = 27 rem 027 ÷ 2 = 13 rem 113 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 03 ÷ 2 = 1 rem 11 ÷ 2 = 0 rem 1

54 = 1101102

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 54.75 to a binary number.

.75 • 2 = 1.5.5 • 2 = 1.0

54 ÷ 2 = 27 rem 027 ÷ 2 = 13 rem 113 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 03 ÷ 2 = 1 rem 11 ÷ 2 = 0 rem 1

54 = 1101102

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 54.75 to a binary number.

54 ÷ 2 = 27 rem 027 ÷ 2 = 13 rem 113 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 03 ÷ 2 = 1 rem 11 ÷ 2 = 0 rem 1

54 = 1101102

.75 • 2 = 1.5.5 • 2 = 1.0

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 54.75 to a binary number.

54 ÷ 2 = 27 rem 027 ÷ 2 = 13 rem 113 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 03 ÷ 2 = 1 rem 11 ÷ 2 = 0 rem 1

54 = 1101102

.75 • 2 = 1.5.5 • 2 = 1.0

.75 = .112

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Binary

How do we convert decimal numbers with a fractional part into binary?

Convert 54.75 to a binary number.

Therefore,54.75 = 110110.112

54 ÷ 2 = 27 rem 027 ÷ 2 = 13 rem 113 ÷ 2 = 6 rem 16 ÷ 2 = 3 rem 03 ÷ 2 = 1 rem 11 ÷ 2 = 0 rem 1

54 = 1101102

.75 • 2 = 1.5.5 • 2 = 1.0

.75 = .112

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How do we convert decimal numbers with a fractional part into hexadecimal?

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How do we convert decimal numbers with a fractional part into hexadecimal?Convert 3973.24 to a hexadecimal number.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How do we convert decimal numbers with a fractional part into hexadecimal?Convert 3973.24 to a hexadecimal number.

From our earlier work today, we know that

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How do we convert decimal numbers with a fractional part into hexadecimal?Convert 3973.24 to a hexadecimal number.

From our earlier work today, we know that3973 = F8516

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How do we convert decimal numbers with a fractional part into hexadecimal?Convert 3973.24 to a hexadecimal number.

From our earlier work today, we know that3973 = F85160.24 = . 3D70A16

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Decimal to Hexadecimal

How do we convert decimal numbers with a fractional part into hexadecimal?Convert 3973.24 to a hexadecimal number.

From our earlier work today, we know that3973 = F85160.24 = . 3D70A16

Therefore,3973.24 = F85.3D70A16