Decimal and Binary Number
The number of base or radix ten is called decimal numbers. It is first number system in which all the ancient and modern mathematical calculation is done. Binary numbers are used to run computer. This note contains description on Decimal and Binary Number system are used to operate computer.
Summary
The number of base or radix ten is called decimal numbers. It is first number system in which all the ancient and modern mathematical calculation is done. Binary numbers are used to run computer. This note contains description on Decimal and Binary Number system are used to operate computer.
Things to Remember
- From the number various other numbers are derived and developed. These numbers are binary numbers, octal numbers, hexadecimal numbers etc.
- The number of base or radix ten is called decimal numbers It is first number system in which all the ancient and modern mathematical calculation is done.
- Binary Number is a number of two base numbers. It is represented by 1 and 0. 1 or 0 is called Binary digits.
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Decimal and Binary Number
Number System
History of number starts from primitive age of human being. The development of number system has integrated with the development of human beings. In primitive age, people used to count stones and pebbles. Hindu philosophers have developed the number system called decimal numbers. From the number various other numbers are derived and developed. These numbers are binary numbers, octal numbers, hexadecimal numbers etc.
Decimal (Denary) Numbers
The number of base or radix ten is called decimal numbers It is first number system in which all the ancient and modern mathematical calculation is done. Other number system is derived from this number. It is generated with the combination of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. We can represent these numbers with suffix two. Eg (9810)10 The following chart displays relations among several number systems derived from the decimal number.
| Base | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |
Hexadecimal | 16 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | |
Decimal | 10 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |||||||
Octal | 8 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |||||||||
Binary | 2 | 0 | 1 |
Binary Number
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 | Binary |
0 | 0 |
1 | 1 |
2 | 10 |
3 | 11 |
4 | 100 |
5 | 101 |
6 | 110 |
7 | 111 |
8 | 1000 |
9 | 1001 |
Conversion of Binary to Decimal and vice-versa
We multiply each binary digit by its weighted position, and add each of the weighted value together.
Weighted value:25 | 24 | 23 | 22 | 21 | 20 |
32 | 16 | 8 | 4 | 2 | 1 |

To convert decimal number to binary number,repeated division by two is needed.
Examples: Convert following into binary numbers:
- (45)10= (101101)2
2 45 1 2 22 0 2 11 1 2 5 1 2 2 0 1 =(101101)2
- (225)10= (10111001)2
2 225 1 2 112 0 2 56 0 2 23 1 2 11 1 2 5 1 2 2 0 1 = (10111001)2
Lesson
Number System
Subject
Computer
Grade
Grade 9
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