Numbering Systems

This article is based on the different numbering systems we have. Every number can be represented as the sum of increasing powers of another number. This is the basic principle of every numbering system. The numbering system we generally use is known as the Decimal System. In this system we use the base number as 10.

Eg. 379 can be represented as (3x100) + (7x10) + (9x1). In this example the increasing powers of 10 are used.

In the above example, if we use 2 instead of 10, it will constitute the Binary System.

Eg. 379 can be represented as (1x256) + (0x128) + (1x64) + (1x32) + (1x16) + (1x8) + (0x4) + (1x2) + (1x1). In this example the increasing powers of 2 are used.

In the above examples, if we use 8 or 16 as base numbers, it will form the Octal and Hexadecimal Systems respectively. It is mandatory to consider A, B, C and so on after 9 for higher systems. To convert a decimal number into another system divide it continuously with the base number and write the remainders from right to left.

Eg. 63 when divided with 16 gives a remainder 15(F) and a quotient 3. 3 cannot be divided by 16, so remainder is 3. Therefore the number in hexadecimal system is 3F.

To convert a number from any system into decimal, multiply it with powers of the base number starting from 1 from right to left.

Eg. 110001 in binary system is (1x1) + (0x2) + (0x4) + (0x8) + (1x16) + (1x32) which is 49 in decimal system.