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Number Systems in a Computer - Computer Fundamentals, Computer Awareness | Famous Books for UPSC Exam (Summary & Tests) PDF Download
Number Systems in a Computer
A set of values used to represent different quantities is known as Number System. For example, a number system can be used to represent the number of students in a class or number of viewers watching a certain TV program etc. The digital computer represents all kinds of data and information in binary numbers. It includes audio, graphics, video, text and numbers. The total number of digits used in a number system is called its base or radix. The base is written after the number as subscript.
Some important number systems are as follows.
- Decimal number system
- Binary number system
- Octal number system
- Hexadecimal number system
Decimal number System
The Decimal Number System consists of ten digits from 0 to 9. These digits can be used to represent any numeric value. The base of decimal number system is 10. It is the most widely used number system. The value represented by individual digit depends on weight and position of the digit.
Binary Number System
Digital computer represents all kinds of data and information in the binary system. Binary Number System consists of two digits 0 and 1. Its base is 2. Each digit or bit in binary number system can be 0 or 1. A combination of binary numbers may be used to represent different quantities like 1001. The positional value of each digit in binary number is twice the place value or face value of the digit of its right side. The weight of each position is a power of 2.
Octal Number System
Octal Number System consists of eight digits from 0 to 7. The base of octal system is 8. Each digit position in this system represents a power of 8. Any digit in this system is always less than 8. Octal number system is used as a shorthand representation of long binary numbers. The number 6418 is not valid in this number system as 8 is not a valid digit.
Hexadecimal Number System
The Hexadecimal Number System consists of 16 digits from 0 to 9 and A to F. The alphabets A to F represent decimal numbers from 10 to 15. The base of this number system is 16. Each digit position in hexadecimal system represents a power of 16. The number 76416 is valid hexadecimal number. It is different from 76410 which is seven hundred and sixty four. This number system provides shortcut method to represent long binary numbers.
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FAQs on Number Systems in a Computer - Computer Fundamentals, Computer Awareness - Famous Books for UPSC Exam (Summary & Tests)
| 1. What are number systems in a computer? |  |
Ans. Number systems in a computer are different ways of representing and manipulating numbers. Computers primarily use the binary number system, which consists of only two digits: 0 and 1. However, other number systems like decimal, octal, and hexadecimal are also used in computer programming and data representation.
| 2. Why do computers use the binary number system? | |
Ans. Computers use the binary number system because it aligns with the fundamental behavior of electronic circuits, which can be either on or off. The binary system simplifies the representation of data and makes it easier for computers to process and store information using electronic components.
| 3. What is the decimal number system? | |
Ans. The decimal number system is a base-10 number system that we use in our daily lives. It consists of ten digits, from 0 to 9, and each digit's position represents a power of 10. Computers often convert numbers from other number systems, such as binary or hexadecimal, to decimal for human-readable output.
| 4. How does the octal number system work in computers? | |
Ans. The octal number system is a base-8 number system that uses eight digits, from 0 to 7. In computers, octal numbers are commonly used in programming as a concise way to represent groups of binary digits. Each octal digit corresponds to a sequence of three binary digits, making it easier to work with binary data.
| 5. What is the hexadecimal number system used for in computers? | |
Ans. The hexadecimal number system is a base-16 number system that uses sixteen digits: 0-9 and A-F. It is widely used in computer programming and digital systems for various purposes. Hexadecimal numbers can represent binary data more compactly, making them easier to read and work with. They are also commonly used in memory addresses and color representations in computer graphics.
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