Base of a Number System :
Base or radix of a number system is defined as the number of digits used to represent the number system. Example decimal number system uses ten digits (0,1,2,3,4,5,6,7,8,9) so, its base is 10. The base of number system is indicated by a subscript and followed by the value of the number.
(1101)2 is of base 2 number system.
(1607)8 is of base 8 number system.
(1809)10 is of base 10 number system.
(190F)16 is of base 16 number system.
Types of Number System :
There are different types of number system. We are going to know about four types of number systems. Depending upon the base of number, number systems are categorized into the followings:
Decimal or Denary Number System
Binary Number System
Octal Number System
Hexadecimal Number System
Decimal or Denary Number System:
A number system that uses ten different digits is known as Decimal Number System. It is also known as Base-Ten number system. The digits of decimal number system are 0,1,2,3,4,5,6,7,8 and 9. The decimal number system is used in our daily life but not used in a computer. The other numbers in the decimal number system are formed by combining its two or more digits like 11 (combination of 1 and 1), 123(combination of 1, 2 and 3). A decimal number can be expressed by using powers of 10.
For example, a decimal number 345 can be expressed as:
345 = 300 + 40 + 5
= 3 x 100 + 4 x 10 + 5 x 1
= 3 x 102 + 4 x 101 + 5 x 100
The number 3, 4 and 5 are the face values of 345. The number 1, 10 and 100 represent place values of 345.
Binary Number System:
A Binary Number System uses two different digits: 0 (zero) and 1 (none zero). It is also known as Base-Two number system. Each digit of the binary number system is called Binary Digit (BIT). The other numbers in the binary number system are formed by combining its digits two or more times like 11(combination of 1 and 1), 101(combination of 1, 0 and 1). The binary number is read digit by digit. For example a binary number 1001 is read as one zero zero one.
A computer is based on two states of electricity(i.e. On or Off) which can be only represented by the binary number system. The 0 bit represents Off state and the 1 bit represents On state of electricity. So, the binary number system is used in the computer to represent data and instructions.
The place values in the binary number can be expressed by using powers of 2 like 20, 21, 22, 23, etc. When you express the binary number by using powers of 2, you get equivalent decimal number.
For example: a binary number 1110 can be expressed as:
(1110)2 = 1 x 23 + 1 x 22 +1 x 21 + 0 x 20
= 8 + 4 + 2 + 0
= 14
Therefore (1110)2 is equivalent to (14)10.
