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 The number system is a way to represent or express numbers. You have heard of various types of number systems such as the whole numbers and the real numbers. But in the context of computers, we define other types of number systems. They are:

• The decimal number system

• The binary number system

• The octal number system and

• The hexadecimal number system

Decimal Number System (Base 10)

In this number system, the digits 0 to 9 represents numbers. As it uses 10 digits to represent a number, it is also called the base 10 number system. Each digit has a value based on its position called place value. The value of the position increases by 10 times as we move from right to left in the number.

For example, the value of 786 is

= 7 x 102 + 8 x 101 + 6 x 100

= 700 + 80 + 6

Binary Number System (Base 2)

A computer can understand only the “on” and “off” state of a switch. These two states are represented by 1 and 0. The combination of 1 and 0 form binary numbers. These numbers represent various data. As two digits are used to represent numbers, it is called a binary or base 2 number system.

The binary number system uses positional notation. But in this case, each digit is multiplied by the appropriate power of two based on its position.

For example, (101101)2 in decimal is

= 1 x 25 + 0 x 24 + 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20

= 1 x 32 + 0 x 16 + 1 x 8 + 1 x 4 + 0 x 2 + 1 x 1

= 32 + 8 + 4 + 1

= (45)10