You may have noticed that 0111 1111
is one less than 1000 0000,
which is 128. So 0111 1111 represents of 12710.
| Binary | Decimal | Notes |
|---|---|---|
| 00000001 | 1 | |
| 00000010 | 2 | 1 × 2 |
| 00000100 | 4 | 2 × 2 |
| 00001000 | 8 | 4 × 2 |
| 00000011 | 3 | |
| 00000110 | 6 | 3 × 2 |
| 00001100 | 12 | 6 × 2 |
| 00011000 | 24 | 12 × 2 |
| 00000111 | 7 | |
| 00001110 | 14 | 7 × 2 |
| 00011100 | 28 | 14 × 2 |
| 00111000 | 56 | 28 × 2 |
If a number is represented with all ones on the right
and all zeros on the left, like this: 0011 1111.
To find the decimal equivalent,
turn on the bit to the left of the left-most one and then
turn off all other bits.
Compute the decimal equivalent of
the resulting pattern and then subtract one.
For example,
the equivalent of 0011 1111 is 0100 0000 - 1.
The decimal value corresponding to the single "on" bit
is 64
and 64 - 1 = 63.
Here is another table of bit patterns (regarded as representing positive integers) and their decimal equivalent. See if you can notice something interesting.
The bit pattern 0011 0010 represents 5010. What bit pattern represents 10010