| Power of 2 | 3 | 2 | 1 | 0 | . | -2 | -3 | -4 | -5 |
|---|---|---|---|---|---|---|---|---|---|
| Decimal | 8 | 4 | 2 | 1 | . | 0.5 | 0.25 | 0.125 | 0.0625 |
| Include? | 0 | 1 | 1 | 0 | . | 1 | 0 | 0 | 1 |
= 4 + 2 + 0.5 +0.0625 = 6.5625
Here is another number: 00010100.
This expression represents
decimal 1.25.
Here is the familiar binary addition algorithm
performed with the two bit patterns, and the usual decimal
addition performed with their decimal equivalent.
| fixed point | as decimal | 01101001 | 6.5625 | 00010100 | 1.2500 | 01111101 | 7.8125 |
Of course, the question is, does the sum of the fixed point expressions (01111101) represent the sum of the decimal expressions (7.8125)?
| Power of 2 | 3 | 2 | 1 | 0 | . | -2 | -3 | -4 | -5 |
|---|---|---|---|---|---|---|---|---|---|
| Decimal | 8 | 4 | 2 | 1 | . | 0.5 | 0.25 | 0.125 | 0.0625 |
| Include? | 0 | 1 | 1 | 1 | . | 1 | 1 | 0 | 1 |
You can satisfy your burning curiosity by adding up the included decimals in the table.