How To Mathematically Convert and Calculate Binary Value To Decimal Value
When converting binary the easiest way is to write out a vertical list in a format like below and follow the formula in the table.
Example Convert 1101 1111 to decimal.
Step 1.)
Write out the binary below in vertical form (leave lots of space on the left side).
Keep this in mind that the "previous sum" starts at 0 on your first line.
Step 2.)
Formula:
2 * Previous Sum + Binary Number = Current Total
Write out each line in order from top to bottom of 1101 1111 in the same format and perform the calculations below.
Note that we alway use 0 for the previous sum.
| 2 | * | Previous Sum | + |
Binary Value |
= | Current Total |
| 2 | * | 0 | + | 1 | = | 1 |
2 |
* | 1 | + | 1 | = | 3 |
| 2 | * | 3 | + | 0 | = | 6 |
| 2 | * | 6 | + | 1 | = | 13 |
| 2 | * | 13 | + | 1 | = | 27 |
| 2 | * | 27 | + | 1 | = | 55 |
| 2 | * | 55 | + | 1 | = | 111 |
| 2 | * | 111 | + | 1 | = | 223 |
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