Number System

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 questions.

Table of Contents:

What is Number System in Maths?

A number system is defined as a system of writing for expressing numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner. It provides a unique representation of every number and represents the arithmetic and algebraic structure of the figures. It also allows us to operate arithmetic operations like addition, subtraction, and division.

The value of any digit in a number can be determined by:

  • The digit
  • Its position in the number
  • The base of the number system

Types of Number System

There are various types of the number system in mathematics. The four most common number system types are:

  1. Decimal number system (Base- 10)
  2. Binary number system (Base- 2)
  3. Octal number system (Base-8)
  4. Hexadecimal number system (Base- 16)

Decimal Number System (Base 10 Number System)

Decimal number system has base 10 because it uses ten digits from 0 to 9. In the decimal number system, the positions successive to the left of the decimal point represent units, tens, hundreds, thousands and so on. This system is expressed in decimal numbers. The base of the decimal is 10. This shows that there are ten symbols, 0 to 9. Similarly, the system using the symbols 0, 1, two will be of base 3, four symbols will be of base 4 and so on.

Every position shows a particular power of the base (10). For example, the decimal number 1457 consists of the digit 7 in the units position, 5 in the tens place, 4 in the hundreds position, and 1 in the thousands place whose value can be written as

(1×1000) + (4×100) + (5×10) + (7×1)

(1×103) + (4×102) + (5×101) + (7×1)

1000 + 400 + 50 + 7

1457

Binary Number System (Base 2 Number System)

The base 2 number system is also known as the Binary number system wherein, only two binary digits exist, i.e., 0 and 1. Specifically, the usual base-2 is a radix of 2. The figures described under this system are known as binary numbers which are the combination of 0 and 1. For example, 110101 is a binary number.

We can convert any system into binary and vice versa.

For Example, to write (14)10 as a binary number.

Solution:

Base 2 Number System Example

Base 2 Number System Example

∴ (14)10 = 11102

Octal Number System (Base 8 Number System)

In the octal number system, the base is 8 and it uses numbers from 0 to 7 to represent numbers. Octal numbers are commonly used in computer applications. Converting an octal number to decimal is same as decimal conversion and is explained below using an example.

Example: Convert 2158 into decimal.

Solution:

2158 = 2 × 82 + 1 × 81 + 5 × 80

= 2 × 16 + 1 × 8 + 5 × 1

= 4510

Hexadecimal Number System (Base 16 Number System)

In the hexadecimal system, numbers are written or represented with base 16. In the hex system, the numbers are first represented just like in deciamal system i.e. from 0 to 9. Then, the numbers are represented using the alphabets from A to F. The below-given table shows the representation of numbers in the hexadecimal number system.

Hexadecimal

0 1 2 3 4 5 6 7 8 9 A B C D E F
Decimal 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

15

Number System Chart

In the number system chart, the bse values, and the digits of different number system can be found. Below is the char of the numeral system.

Number System Chart

Number System Chart

Number System Conversion

Numbers can be represented in any of the number system categories like binary, decimal, hex, etc. Also, any number which is represented in any of the number system types can be easily converted to other. Check the detailed lesson on the conversions of number systems to learn how to convert numbers in decimal to binary and vice versa, hexadecimal to binary and vice versa, and octal to binary and vice versa using various examples.

Video Lesson on Numeral System

Number System Questions

  1. Convert (242)10 into hexadecimal. [Answer: (F2)16]
  2. Convert 0.52 into an octal number. [Answer: 4121]
  3. Subtract 11012 and 10102. [Answer: 0010]
  4. Represent 5C6 in decimal. [Answer:1478] 
  5. Represent binary number 1.1 in decimal. [Answer: 1.5]

Also Check: Binary Operations

Computer Numeral System (Number System in Computers)

When we type any letter or word, the computer translates them into numbers since computers can understand only numbers. A computer can understand only a few symbols called digits, and these symbols describe different values depending on the position they hold in the number. In general, the binary number system is used in computers. However, the octal, decimal and hexadecimal systems are also used sometimes.

More Topics Related to Number Systems

Frequently Asked Questions

What is Number System and its Types?

The number system is simply a system to represent or express numbers. There are various types of number systems and the most commonly used ones are decimal number system, binary number system, octal number system, and hexadecimal number system.

Why the Number System is Important?

Number system helps to represent numbers in a small symbol set. Computers, in general, use binary numbers 0 and 1 to keep the calculations simple and to keep the amount of necessary circuitry less which results in the least amount of space, energy consumption, and cost.

What is Base 1 Number System Called?

Base 1 number system is called the unary numeral system and is the simplest numeral system to represent natural numbers.

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