Decimal

to

Binary Conversion

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27 26 25 24 23 22 21 20

128 64 32 16 8 4 2 1

1

Use the chart to record the subtraction

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Method 1 - subtraction

To convert the decimal number 189 to binary you must subtract the highest number possible first. Place a 1 in the chart for any number you subtract.

189

-128

61

Cannot subtract a 64

61

- 32

29

29

- 16

13

13

- 8

5

1 10 1 1 10

5

- 4

1

1

- 1

0

Cannot subtract a 2

= 189

27 26 25 24 23 22 21 20

128 64 32 16 8 4 2 1

0

Use the chart to record the subtraction

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Try another number using Method 1 - subtraction

To convert the decimal number 75 to binary you must subtract the highest number possible first. Place a 1 in the chart for any number you subtract.

Cannot subtract a 128

75

- 64

11

Cannot subtract a 32

Cannot subtract a 16

11

- 8

3

0 01 1 0 11

Cannot subtract a 4

1

- 1

0

3

- 2

1

= 75

27 26 25 24 23 22 21 20

128 64 32 16 8 4 2 1

1

Press any key to continue…

On a piece of paper convert the number 242 using Method 1 – subtraction. Press any key when you have an answer.

To convert the decimal number 242 to binary you must subtract the highest number possible first. Place a 1 in the chart for any number you subtract.

242

- 128

114

114

- 64

50

50

- 32

18

18

- 16

2

Cannot subtract an 8

1 11 0 0 01

Cannot subtract a 4

2

- 2

0

= 242

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Method 2 - division

Use the chart to record the division

27 26 25 24 23 22 21 20

128 64 32 16 8 4 2 1

To convert the decimal number 189 to binary you must divide the number by 2. Starting from the right, place a 1 if there is a remainder or a 0 if no remainder.

189 / 2 = 94 r 1 94 / 2 = 47 r 0 47 / 2 = 23 r 1 23 / 2 = 11 r 1 11 / 2 = 5 r 1 5 / 2 = 2 r 1 2 / 2 = 1 r 0

01101 1 1 1 = 189

1 / 2 = cannot divide further - carry the 1

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Method 2 - division

Use the chart to record the division

27 26 25 24 23 22 21 20

128 64 32 16 8 4 2 1

To convert the decimal number 75 to binary you must divide the number by 2. Starting from the right, place a 1 if there is a remainder or a 0 if no remainder.

75 / 2 = 37 r 1 37 / 2 = 18 r 1 18 / 2 = 9 r 0 9 / 2 = 4 r 1 4 / 2 = 2 r 0 2 / 2 = 1 r 0

10010 1 0 1 = 75

1 / 2 = cannot divide further - carry the 1 Fill in to make 8 bits with 0

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Method 2 - division

Use the chart to record the division

27 26 25 24 23 22 21 20

128 64 32 16 8 4 2 1

To convert the decimal number 242 to binary you must divide the number by 2. Starting from the right, place a 1 if there is a remainder or a 0 if no remainder.

242 / 2 = 121 r 0121 / 2 = 60 r 1 60 / 2 = 30 r 0 30 / 2 = 15 r 0 15 / 2 = 7 r 1 7 / 2 = 3 r 1 3 / 2 = 1 r 1 1 / 2 = cannot divide further - carry the 1

11111 0 0 0 = 242

The End