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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...
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Binary Place Values |
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D7 |
D6 |
D5 |
D4 |
D3 |
D2 |
D1 |
D0 |
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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 |
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i.e. Decimal 150 = Binary 10010110 |
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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 MS Word format here