| 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 |
Answer:
Adding up the "turned on" powers of two gives:
128 + 32 + 8 + 2 = 17010
| 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.
| 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 |
Look at the table and see if you can discover a useful pattern.
An important number was left out of the
table. What do you suppose is the decimal equivalent of