Computer number system and types of number system

What are the number systems in Computer?

computer number system is the internal representation of numeric values in digital computer and calculator hardware and software. Normally, numeric values are stored as groupings of bits, named for the number of bits that compose them. The encoding between numerical values and bit patterns is chosen for convenience of the operation of the computer; the bit format used by the computer’s instruction set generally requires conversion for external use such as printing and display.

numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

Types of computer number system

Below are the list of computer number systems which computer architecture supported as of now:

  • Binary number system — Represent any number using 2 digits [0–1]
  • Octal number system — Represent any number using 8 digits [0–7]
  • Decimal number system — Represent any number using 10 digits [0–9]
  • Hexadecimal (hex) number system — Represent any number using 10 digits and 6 characters [0–9, A, B, C, D, E, F]

1. What is binary number system?

A Binary Number is made up of only 0s and 1s. It’s look like 110100. Below is an example of binary number system.

binary number system

2. What is octal number system?

The octal numeral system is the base-8 number system, and uses the digits from 0 to 7.  The Octal Numbering System is very similar to hexadecimal numbering system. Octal numerals can be made from binary numerals by grouping consecutive binary digits into groups of three (starting from the right).

For example, the binary representation for decimal 74 is 1001010. Two zeroes can be added at the left: (00)1 001 010, corresponding the octal digits 1 1 2, yielding the octal representation 112.

Representation of an octal number system

Representation of an Octal Number

Here is c program to convert binary to Octal number.

3. What is decimal number system?

The decimal numeral system is the standard number system for denoting the integer and non-integer numbers. It is also called Hindu-Arabic, or Arabic, number system numeral system.

The way of denoting numbers in the decimal system is often referred to as decimal notation. Decimal number system, we use every day, based on 10 digits (0,1,2,3,4,5,6,7,8,9). Below is an example of decimal number system:

  1. 786 is written as 7 103 + 8 102 + 6 100.
  2. 101101 = 1 x 25 + 0 x 24 + 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20 = 1 x 32 + 0 x 16 + 1 x 8 + 1 x 4 + 0 x 2 + 1 x 1 = 32 + 8 + 4 + 1

Here is c program to convert binary to decimal number.

4. What is hexadecimal (hex) number system?

The hexadecimal numeral system, often shortened to “hex”, is a numeral system made up of 16 symbols. It uses the decimal numbers and six extra symbols. There are no numerical symbols that represent values greater than nine, so letters taken from the English alphabet are used, specifically A, B, C, D, E and F. Hexadecimal A = decimal 10, and hexadecimal F = decimal 15.

Hexadecimal numeral system example:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F;

Below table will explain the hexadecimal numeral and its decimal values.

hexadecimal numeral system

Here is c program to convert binary to hexadecimal number.


  2. Number Conversion Programs in C

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