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
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:
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