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Converting Decimal to Binary

Converting from Decimal to Binary is a little bit harder than going the other way. If you follow the steps you will have no problems.

To change from Decimal to Binary you carry out a series of subtractions based on the Binary 'Place' values...

Binary Place Values
D7 D6 D5 D4 D3 D2 D1 D0
128 64 32 16 8 4 2 1

Consider decimal 150...

Step 1 Subtract 128   150 - 128 = 22
Since 150 'contained' 128, D7 is "1". The binary number so far is: 1 X X X X X X X

Step 2 Subtract 64 from 22   Can't. D6 is zero. The binary number so far is: 1 0 X X X X X X

Step 3 Subtract 32 fom 22    Can't. D5 is zero. The binary number so far is: 1 0 0 X X X X X

Step 4 Subtract 16   22 - 16 = 6 
Since 150 'contained' 16,  D4 is "1". The binary number so far is: 1 0 0 1 X X X X

Step 5 Subtract 8 from 6    Can't. D3 is zero. The binary number so far is: 1 0 0 1 0 X X X

Step 6 Subtract 4 from 6    6 - 4 = 2 
Since 150 'contained' 4, D2 is "1".The binary number so far is: 1 0 0 1 0 1 X X

Step 7 Subtract 2 from 2    2 - 2 = 0
Since 150 'contained' 2, D1  is "1". The binary number so far is: 1 0 0 1 0 1 1 X
NOTE: You need to be careful you don't write down zero at this point.

Step 8 Subtract 1 from 0    Can't. D0 is zero. The binary number is: 1 0 0 1 0 1 1 0

i.e. 150 decimal is 10010110 binary.

Decimal to Binary Conversion Table

Decimal
Number
Place
Value
  Balance Binary Number ("X" = unknown)
150 - 128 OK = 22 1 X X X X X X X
22 - 64 can't = 22 1 0 X X X X X X
22 - 32 can't = 22 1 0 0 X X X X X
22 - 16 OK = 6 1 0 0 1 X X X X
6 - 8 can't = 6 1 0 0 1 0 X X X
6 - 4 OK = 2 1 0 0 1 0 1 X X
2 - 2 OK = 0 1 0 0 1 0 1 1 X
0 - 1 can't = 0 1 0 0 1 0 1 1 0
 
i.e. Decimal 150 = Binary 10010110

You should check your answer by doing a Binary to Decimal conversion...

10010110 = 128 + 0 + 0 + 16 + 0 + 4 + 2 + 0 = 150

Open the worksheet table above in Word format HERE

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