Ppt on number system

NUMBER SYSTEMTHE FOLLOWING PPT COVERS THE FOLLOWING THINGS: INTRODUCTION WHAT IS A DECIMAL

NUMBER? WHAT IS A BINARY

NUMBER? conversion of binary to

decimal and vice-versa conversion of octal to

decimal and vice-versa

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INTRODUCTIONA number system defines how a number can be represented using distinct symbols. A number can be represented differently in different systems. For example, the two numbers (2A)16 and (52)8 both refer to the same quantity, (42)10, but their representations are different.

A binary number is a number that includes only ones and zeroes.

Another name for binary is base-2 ( "base two") .

Computers store information using binary numbers

It is the building block of all dataIn order to understand storage capacity and sizes, you need to know how data is read and saved

In Binary we count in the opposite direction 8421.

What is a binary number?

=

1. The first position value is 20 , i.e. one2. The 2nd position value is 21 , i.e. two3. The 2nd position value is 22 , i.e. four4. The 2nd position value is 23 , i.e. eight5. The 2nd position value is 24 , i.e.

sixteen etc.

CONVERSION OF BINARY

TO DECIMAL

The value of binary 01100001 is decimal 105. This is worked out below:

----------------------------------------------------------------------0 1 1 0 1 0 0 1

1 X 1 = 10 X 2 = 00 X 4 = 01 X 8 = 80 X 16 = 01 X 32 = 321 X 64 = 64

0 X 128 = 0----Answer: 105

EXAMPLE

7

The numbers that we are used to seeing are called decimal numbers.

Decimal numbers consist of the digits from 0 (zero) through 9.

Another name for decimal numbers are base-10 (pronounced "base ten") numbers.

WHAT IS A DECIMAL NUMBER?

8

S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

CONVERSION OF DECIMAL TO BINARY

What is octal number ? Octal digits have place values based on

the value 8. The octal numbering system includes

eight base digits ( 0, 1, 2, 3, 4, 5, 6, 7 ) Computer scientists are often looking for

shortcuts to do things. One of the ways in which we can

represent binary numbers is to use their octal equivalents instead.

This is especially helpful when we have to do fairly complicated tasks using numbers.

CONVERSION OF OCTAL TO DECIMAL

NUMBER 1. In the number 111 base 8, the digit farthest to the right is in the “ones” place and is worth 1. Technically this is the 80

place.2. The 2nd digit from the right, 111, is in the “eights” place, the

“base” place, and is worth 8. Technically this is the 81 place.3. The 3rd digit from the right, 111, is in the “sixty-fours” place,

the “base squared” place, and is worth 64.Technically this is the 82 place.

The total value of this octal number, 111, is 64+8+1, or seventy-three.

Example: convert the number 111,base 10 to octal.

Conversion of decimal to binary

738

9

1

8

1

17310 = 1118

CONVERSION OF BINARY

TO OCTAL The conversion between binary and octal is quite simple. Since 2 to the power of 3 equals 8, it takes 3 base 2 digits to

combine to make a base 8 digit. 000 base 2 equals 0 base 8

0012 = 18

0102 = 28

0112 = 38

1002 = 48

1012 = 58

1102 = 68

1112 = 78

What if you have more than three binary digits, like 110011?

Just separate the digits into groups of three from the right, then convert each group into the corresponding base 8 digit.

110 011 base 2 = 63 base 8 1100101 = 1 100 101 = 001 100 101

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RISHABH KANTH - PPT SHRIYA PARASHAR SUBHAM LUTHRA SAKSHAM SUNDRANI SANIDHYA KHATRI SHLOK AGRAWAL

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Thanking u 4 looking . May this Ppt helps you.