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

 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

From the rules for positional notation there are two digits in base two. Usually "0" and "1" are chosen, and usually the word bit is used. "Bit" is an abbreviation of "binary digit".

In this system the base, two, is 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. The table shows an example.

The first line in the table is written entirely in base two, and shows what the string "1011" means with positional notation. Both the base its powers are written in base two. The next line uses decimal notation for the base and its powers. The remaining lines use base ten arithmetic until finally the integer is expressed in base ten positional notation.

### QUESTION 13:

What is 0110 (binary representation) in base ten?