Decimal and Binary Number
The number of base or radix ten is called decimal numbers. Similarly, Binary Number is a number of two base numbers.This note provides an information about Decimal and Binary Numbers.
Summary
The number of base or radix ten is called decimal numbers. Similarly, Binary Number is a number of two base numbers.This note provides an information about Decimal and Binary Numbers.
Things to Remember
- The arrangement of number in a computer system is known as computer number system.
- There are different types of computer number system.They are binary number system( have base 2), octal number system(have base 8), decimal number system(have base 10 ) and hexadecimal number system(have base 16).
- Binary Number is a number of two base numbers. It is represented by 1 and 0.
- The number of base or radix ten is called decimal numbers.
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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.
| System | 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.
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
Computer Number System
Subject
Computer Science
Grade
Grade 10
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