What is Number System? Different Types of Number System | Number System Explained

The number system or the numeral system is the system of naming or representing numbers. There are various types of number systems in maths like binary, decimal, etc. This lesson covers the entire concepts of the numeral system with their types, conversions and question. Generally, It is set of rules and symbols, used to represent a number.

The number system can be classified into weighted (or positional) and non-weighted (or non-positional)systems. Most of the number systems are of weighted type. The knowledge of number system is very essential because the design and of a computer is dependent upon the number systems.

Number Systems are two types: 

1.Non Positional Number System.

2. Positional Number System.

 1. Non-weighted or Non-Positional Number Systems

In early days, human begins counted on fingers. When ten fingers were not adequate, stones, pebbles, or sticks were used to indicate values. This method of counting uses an additive approach or the non-positional number system.

 In this system, we have symbols such as I for 1, II for 2, III for 3, IIII for 4, III for 5, etc. Each symbol represents the same value regardless of its position in the number and the symbols are simply added to find out the value of a particular number. Since it is very difficult to perform arithmetic with such a number system, positional systems were developed.

2. Weighted or Positional Number Systems

In a positional number system, there are only a few symbols called digits, and these symbols represent different values depending on the position they occupy in the number. 

The value of each digit in such a number is determined by three considerations:

1. The digit itself.

2. The position of the digit in the number.

3. The base of the number system. In weighted number systems.

 

The four most common number system types are:

• Decimal number system (Base- 10).

• Binary number system (Base- 2).

• Octal number system (Base-8).

• Hexadecimal number system (Base- 16).

Decimal Number System(Base-10)

Decimal Number System is a Base 10 Number System having 10 digits from 0 to 9. This means that any numerical quantity can be represented using these 10 digits. Decimal number system is also a positional value system. This means that the value of digits will depend on its position.

If you want to learn more about DECIMAL NUMBER SYSTEM, then Checkout our other article:

• Decimal number system by Quicky Tech

Binary number system (Base- 2)

In mathematics and digital electronics, a binary number is a number expressed in the base- 2 numeral system or binary number system which uses only two symbols: typically "0" (zero) and "1" (one). The base-2 numeral system is a positional notation with a radix of 2.

Uses of Binary Number System

Computer systems use electronic circuits which exist in only one of two states the binary number system is a method of representing numbers that counts by using combinations of only two numerals: zero (0) and one (1). The computer's only recognizes two states, on or off. Binary simplifies information processing. Because there must always be at least two symbols for a processing system to be able to distinguish significance or purpose, binary is the smallest numbering system that can be used.

Characteristics of binary number system are as follows

➧Uses two digits, 0 and 1.

➧Also called base 2 number system

➧Each position in a binary number represents a 0 power of the base (2). Example 2⁰

➧Last position in a binary number represents a x power of the base (2). Example 2* where x represents the last position - 1.

Note: 101012 is normally written as 10101.

If you want to learn more about BINARY NUMBER SYSTEM, then Checkout our other article:

• Binary Number System by Quicky Tech

Octal number system (Base-8)

The octal numeral system or oct for short, is the base-8 number system, and uses the digits 0 to 7. 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.

Characteristics of octal number system are as follows:

➧Uses eight digits; 0, 1, 2, 3, 4, 5, 6, 7.
➧Also called base 8 number system.
➧Each position in an octal number represents a 0 power of the base (8). Example 80
➧Last position in an octal number represents a x power of the base (8). Example 8 where x represents the last position - 1.

Example. Octal Number: 125708

If you want to learn more about OCTAL NUMBER SYSTEM, then Checkout our other article:

• Octal Number System by Quicky Tech

Hexadecimal number system (Base- 16):

The hexadecimal number system often shortened to " hex", is a numeral system made up of 16 symbols (base 16). The standard numeral system is called decimal (base 10) and uses ten symbols: 0,1,2,3,4,5,6,7,8,9. Hexadecimal uses the and six extra symbols.16 is the base of this system. Hexadecimal Number System.

Characteristics of hexadecimal number system are as follows: 

➧Uses 10 digits and 6 letters; 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. Letters represents numbers starting from 10. A 10. B 11, C-12, D-13, E - 14, F = 15.

➧Also called base 16 number system.

➧Each position in a hexadecimal number represents a 0 power of the base (16).

➧Last position in a hexadecimal number represents a x power of the base (16). Example 16* where x represents the last position -1.

If you want to learn more about OCTAL NUMBER SYSTEM, then Checkout our other article:

• Hexadecimal Number System by Quicky Tech

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