## Note on Number system

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Number system can be defined as the combination of different numbers which helps in the calculation. History of number starts from the primitive age of human being. The development of number system has integrated with the development of human beings. In the primitive age, people used to count stones and pebbles.

#### Binary Numbers

Binary Number is a number of two base numbers. It is represented by 1 and 0. 1 or 0 is called Binary digits.We can generate this number with the combination of 0 and 1. It is represented with suffix two. Eg (10101)2. Following table shows some decimal number and their equivalent binary numbers**.

#### Decimal (Denary) Numbers

The number of base or radix ten is called decimal numbers. It is the first number system in which all the ancient and modern mathematical calculation is done. Another number system is derived from this number. It is generated by the combination of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. We can represent these numbers with suffix two. Eg (9810)10The following chart displays relations among several number systems derived from the decimal number.

#### Octal Numbers

The number with base eight is called octal number. It is represented by Q or O. We can generate these numbers with the combination of 0, 1, 2 3, 4, 5, 6, 7. We can represent these numbers wit suffix eight. Eg (5432)8

The number with base sixteen is called hexadecimal number. We can generate these numbers with the combination of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A,B, C, D, E, F. Where A=10, B=11, C=13, D=14, E=15, F=16. We can represent these numbers with suffix sixteen. E.g. (12AB)16 Where A=10, B=11. The 4-bit format of the binary is used for hexadecimal to binary conversion.

#### **Equivalent values for different number systems

 Decimal Binary Octal Hexadeciamal 0 0 0 0 1 1 1 1 2 10 2 2 3 11 3 3 4 100 4 4 5 101 5 5 6 110 6 6 7 111 7 7 8 1000 10 8 9 1001 11 9 10 1010 12 A 11 1011 13 B 12 1100 14 C 13 1101 15 D 14 1110 16 E 15 1111 17 F

• Number system can be defined as the combination of different numbers which helps in the calculation.
• Binary Number is a number of two base numbers.
• The number of base or radix ten is called decimal numbers.
• The number with base eight is called octal number.
• The number with base sixteen is called hexadecimal number.
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### Very Short Questions

A number system that uses sixteen different digits to represent different values is known as hexadecimal number system. The base of hexadecimal number system is 16 because it consist sixteen digits from 0 to 9 and A to F to represent values from ten to fifteen. The digits A, B, C, D, E and F of hexadecimal number represent the decimal numbers 10, 11, 12, 13, 14 and 16 respectively.

A number system that uses eight different digits to represent different values is known as octal number system. The base of octal number system is 8 because it consist eight digits from 0 to 7. The octal number system is used in the computer to represent binary numbers. The place values in the octal number can be expressed by using powers of 8.

A number system act as the symbols used to express quantities on the basis for counting, comparing amounts, performing calculations, and representing value. The different number system use different digits or symbols to represent numbers. The number of digits used in a number system is known as base of the number system. The different number systems have different base number. The different types of number system are: -

• Decimal Number System
• Binary Number System
• Octal Number System

A number system that uses ten different digits to represent different values is known as decimal number system. The base of decimal number system is 10 because it consist ten digits from 0 to 9. Decimal number can be expressed by using powers of 10.

A number system that uses two different digits to represent different values is known as binary number system. The base of thebinary number system is 2 because it consist two digits 0 and 1. Each digit of the binary number system is called Binary Digit (BIT). The binary number system is used in the computer.

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• ### A number system having two base numbers is ______.

decimal number system
octal number system
Binary number system
• ### The number of base or radix ten is called ______.

hexa decimal number
decimal number
binary number
octal number

10
8
2
5

10
2
20
16
• ### The number with base eight is called ______.

binary number
hexa decimal number
decimal number
octal number

2
10
16
8
• ### The number with base sixteen is called ______.

octal number
binary number
decimal number
hexa decimal number

10
8
2
16