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Binary

Converting to and from decimal

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Decimal

We normally use the decimal (denary) system, also called base 10

There are 10 different symbols (digits) 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 To count higher than nine we re-use the

symbols by putting them in columns The value of a symbol depends on its

position

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Decimal positions

1000 100 10 1

Thousands Hundreds Tens Units

8 2 5 3

Eight thousand two hundred and fifty three

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Binary

Computers use the binary system, also called base 2

There are two different symbols (digits) 0, 1 To count higher than one we re-use the

symbols by putting them in columns The value of a symbol depends on its

position

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Binary positions

8 4 2 1

Eights Fours Twos Units

1 1 0 1

One eight, one four, no twos and one unitThat makes thirteen

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Counting in binary and decimal

0 0 1000 8

1 1 1001 9

10 2 1010 10

11 3 1011 11

100 4 1100 12

101 5 1101 13

110 6 1110 14

111 7 1111 15

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Why do computers use binary?

Computer components that store or handle data are often two-state devices

This is like a switch that can be on or off A memory unit could exist in two voltage

states, high or low A voltage on a cable could be high or low A light could be on or off Two states can be coded by binary 0 and 1

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Why am I learning about binary?

In your Cisco course, you will learn about IP addresses and how to split up a network into subnets

You need to work out subnet addresses and workstation addresses

For this you need to use binary

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Bytes or octets

We often handle binary digits (bits) in groups of eight

Sometimes these groups are called bytes Sometimes they are called octets We shall often be calling them octets Examples of octets:

00101101

10110010

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Convert binary to decimal

Value 128 64 32 16 8 4 2 1

Binary

Convert 11001010 binary to decimalWrite in the binary digits under their values

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Convert binary to decimal

Value 128 64 32 16 8 4 2 1

Binary 1 1 0 0 1 0 1 0

Convert 11001010 binary to decimalWrite in the binary digits under their valuesNext write in the value for each binary 1 digit

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Convert binary to decimal

Value 128 64 32 16 8 4 2 1

Binary 1 1 0 0 1 0 1 0

128 64 8 2

Convert 11001010 binary to decimalWrite in the binary digits under their valuesNext write in the value for each binary 1 digitAdd up the values 128 + 64 + 8 + 2 = 202

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One for you to try

Convert 10010101 from binary (base 2) to decimal (base 10)

Value 128 64 32 16 8 4 2 1

Binary

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Answer

Convert 10010101 from binary (base 2) to decimal (base 10)

Value 128 64 32 16 8 4 2 1

Binary 1 0 0 1 0 1 0 1

128 16 4 1

128 + 16 + 4 + 1 = 149

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Convert 185 decimal to binary

Value 128 64 32 16 8 4 2 1

Binary

Check

Convert 185 decimal to binaryCan you take 128 from 185? Yes.Put 1 under 128What is left? 185-128 = 57

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Convert 185 decimal to binary

Value 128 64 32 16 8 4 2 1

Binary 1

Check

We have 57 leftCan you take 64 from 57? No.Put 0 under 64What is left? Still 57

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Convert 185 decimal to binary

Value 128 64 32 16 8 4 2 1

Binary 1 0

Check

We have 57 leftCan you take 32 from 57? Yes.Put 1 under 32What is left? 57 – 32 = 25

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Convert 185 decimal to binary

Value 128 64 32 16 8 4 2 1

Binary 1 0 1

Check

We have 25 leftCan you take 16 from 25? Yes.Put 1 under 16What is left? 25 – 16 = 9

21 Apr 2023 1919

Convert 185 decimal to binary

Value 128 64 32 16 8 4 2 1

Binary 1 0 1 1

Check

We have 9 leftCan you take 8 from 9? Yes.Put 1 under 8What is left? 9 – 8 = 1

21 Apr 2023 2020

Convert 185 decimal to binary

Value 128 64 32 16 8 4 2 1

Binary 1 0 1 1 1

Check

Wwe have 1 leftCan you take 4 from 1? No.Put 0 under 4What is left? Still 1

21 Apr 2023 2121

Convert 185 decimal to binary

Value 128 64 32 16 8 4 2 1

Binary 1 0 1 1 1 0

Check

We have 1 leftCan you take 2 from 1? No.Put 0 under 2What is left? Still 1

21 Apr 2023 2222

Convert 185 decimal to binary

Value 128 64 32 16 8 4 2 1

Binary 1 0 1 1 1 0 0

Check

We have 1 leftCan you take 1 from 1? Yes.Put 1 under 1What is left? Nothing. Finished.

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Convert 185 decimal to binary

Value 128 64 32 16 8 4 2 1

Binary 1 0 1 1 1 0 0 1

Check

185 decimal is 10111001 binary

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Convert decimal to binary

Value 128 64 32 16 8 4 2 1

Binary 1 0 1 1 1 0 0 1

Check 128 32 16 8 1

Check: write in the values of the 1 digits and add them up128 + 32 + 16 + 8 + 1 = 185That’s the number we started with. It’s correct.

21 Apr 2023 2525

One for you to try

Convert 248 from decimal to binary Check your answer

Value 128 64 32 16 8 4 2 1

Binary

Check

21 Apr 2023 2626

Answer

Convert 248 from decimal to binary Check your answer

Value 128 64 32 16 8 4 2 1

Binary 1 1 1 1 1 0 0 0

Check 126 64 32 16 8

128 + 64 + 32 + 16 + 8 = 248

So 11111000 is correct.

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End