1010 = 1 × 2^{3}+ 0 × 2^{2}+ 1 × 2^{1}+ 0 × 2^{0}= 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 = 9`

,
_{10}`1011 = 11`

, and others.
_{10}

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?