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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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