Decimal to Binary Number Conversion
Converting a known decimal number into its binary equivalent can be accomplished by a simple trial and error method once you are familiar with the weighting sequence of the binary numbers. Suppose that you wish to convert the decimal 175 into its binary equivalent. To do this you first determine the highest positional weight that is equal to or less than the number being converted. This is 128. Subtract 128 from 175 and note the remainder (47). Again, determine the highest positional weight that does not exceed the remainder (32). Determine their difference and continue to repeat the process until no further subtractions are possible.
Example:
- 175-128= 47
- 47-32= 15
- 15-8= 7
- 7-4= 3
- 3-2= 1
- 1-1=0
Binary Numbers by Position
| 128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
| 1 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
Another method (and the most widely used) for converting decimal numbers into binary is to repeatedly divide the number by two (2) and note the remainder. When dividing by 2, the remainder will always be 1 or 0. The remainder forms the equivalent binary number. As an example, convert the number 175 into its binary equivalent. Note: LSB = Least Significant Bit and MSB = Most Significant Bit.
Divide By Two (2) Method
| Decimal # | Divided by | Result | Remainder |
|---|
| 175 |
2 |
87 | 1 |
LSB=1 |
|---|
| 87 |
2 |
43 |
1 |
2 |
|---|
| 43 |
2 |
21 |
1 |
4 |
|---|
| 21 |
2 |
10 |
1 |
8 |
|---|
| 10 |
2 |
5 |
0 |
16 |
|---|
| 5 |
2 |
2 |
1 |
32 |
|---|
| 2 |
2 |
1 |
0 |
64 |
|---|
| 1 |
2 |
0 |
1 |
MSB=128 |
|---|