Binary Numbers

A binary number is a number in base 2. This means that each place can be represented by just two numbers, 0 or 1. You calculate the value of a binary number just as you would in any other base, the most commonly used is what we use everyday, decimal, or base 10.

In decimal numbers we multiply the number in the place by 10 raised to whatever place it is in. For instance a simple example would be the number 349 (Three hundred forty nine). This can be written as:

(3 * 10^2) + (4 * 10^1) + (9 * 10^0) = 3*100 + 4*10 + 9*1 = 349.

As stated above, binary numbers use only 1's and 0's in their places (Decimal numbers use number from 0-9). So to see what the value of a number like:

1010 is in binary we can write it just as we did above except that the base is 2 instead of the 10 used in decimal. So, we would have 1010 as:

(1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0) = 1*8 + 0 + 1*2 + 0 = 10 in decimal.

This numbering system is used in computer systems because an electrical signal inside of your computer can either be on or off. 0 typically represents when there is no electrical signal and 1 represents when their is a charge. This is the foundation of all computer systems.