| Power of 2 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Decimal | 1024 | 512 | 256 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| Include? | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
Adding up the "turned on" powers of two gives:
128 + 32 + 8 + 2 = 17010
Here is a list of positive integers represented in both 8-bit binary and decimal. You will encounter these patterns frequently. For now, only positive integers are represented. Negative integers come later.
Look at the table and see if you can discover a useful pattern.
| Binary | Decimal | Notes |
|---|---|---|
| 0000 0000 | 0 | |
| 0000 0001 | 1 | 20 = 1 = 21 - 1 |
| 0000 0011 | 3 | 21 + 20 = 3 = 22 - 1 |
| 0000 0100 | 4 | 22 |
| 0000 0111 | 7 | 22 + 21 + 20 = 23 - 1 |
| 0000 1000 | 8 | 23 |
| 0000 1111 | 15 | 24 - 1 |
| 0001 0000 | 16 | 24 |
| 0001 1111 | 31 | 25 - 1 |
| 0010 0000 | 32 | 25 |
| 0111 1111 | ? | ? |
| 1000 0000 | 128 | 27 |
An important number was left out of the
table. What do you suppose is the decimal equivalent of
0111 1111 ?