1010 = 1 × 23 + 0 × 22 + 1 × 21 + 0 × 20
= 8 + 0 + 2 + 0
= 10
It
is convenient to remember the above fact.
If you know it, then it takes just a moment to
recognize 1001 = 910,
1011 = 1110, and others.
To convert larger binary representations to decimal representation, use a table. You can create this table from scratch by multiplying the decimal values by two starting on the right.
| 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 |
Think of the bits of the binary representation as turning on or off
the numbers to include in the sum.
For example, with 1010 1010
the various powers are turned on, as above.
A particular number is represented by 1010 1010 (binary representation). What is the number represented in base ten?