Answer:
0110 = 0 × 23 + 1 × 22 + 1 × 21 + 0 × 20
= 0 + 4 + 2 + 0
= 6
0110 = 0 × 23 + 1 × 22 + 1 × 21 + 0 × 20
= 0 + 4 + 2 + 0
= 6
In a binary representation a particular power of two is either included in the sum or not, since the digits are either "1" or "0". In converting representations, it is convenient to have a table.
| 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? |
Here is an 8-bit pattern: 0110 1001. If it represents a number (using binary positional notation), convert the notation to decimal by including the powers of two matching a "1" bit.
Copy 1s from the bit pattern to the last row of the table, starting at the right. Compute the sum of the corresponding decimal numbers.