### A good answer might be:

1. The base is 2.
2. There are 2 "digits": 0, 1.
3. Positions correspond to integer powers of two, starting with power 0 at the rightmost digit, and increasing right to left.
4. The digit placed at a position shows how many times that power of two is included in the number.

# Representing Numbers using Base Two

From the rules for positional notation there are two digits. Usually "0" and "1" are chosen. In this system the base, two, will be written "10", the first power of two plus zero times the zeroth power of two. Each place in a representation stands for a power of two. Often this is called the binary system. Here is an example:

> 1011 | = | 1 × (10)11 | + | 0 × (10)10 | + | 1 × (10)1 | + | 1 × (10)0
> | = | 1 × 23 | + | 0 × 22 | + | 1 × 21 | + | 1 × 20
> | = | 1 × 8 | + | 0 × 4 | + | 1 × 2 | + | 1 × 1
> | = | 8 | + | 0 | + | 2 | + | 1
> | = | 11 |  |  |  |  |  |

The first line above is written entirely in base two, and shows what the string "1011" means with positional notation. Both base its powers are written in base two. The next line writes the base and its powers using decimal notation (this is what is usually done, even though it mixes notation). The remaining lines finish converting the base into decimal.

### QUESTION 13:

What is 0110 (binary representation) in base ten?