The binary system, or base two systems, is a system used to express numbers using only the digits 1 and 0.

The decimal system, or base ten systems, (the system we commonly use), uses the digits 0,1,2,3,4,5,6,7,8,9, and each digit has a different value depending on the position it has in a number. For instance, figure 258 in the decimal system means eight units, plus five tens, plus two hundred. Each position corresponds to a power of ten, 1,10,100,1000,10000, etc.

The binary system is similar in that each digit has a different value depending on the position it has in the number. In the binary system, however, each position corresponds to a power of two 1,2,4,8,16,32, etc, not to a power of 10. And, as said before, it uses only two digits: 1 and 0. For instance, the decimal numbers from zero to ten would be in binary

0

1

10

11

100

101

110

111

1000

1001

1010

It is possible to express numbers in any base. The rule is the same, you use the first n digits (starting from zero) and each position corresponds to a power of the base. For instance, numbers zero to ten in base three would be:

0,1,2,10,11,12,20,21,22,100,101

When the base is greater than 10, you need to begin using letters beside the traditional digits 0-9. Base 16 for instance is commonly used in computer programming, and It uses 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F