What is a Number System?

Answer: A Number system is a method of showing numbers by writing, which is a mathematical way of representing the numbers of a given set, by mathematically using the numbers or symbols.

Number system is important from the viewpoint of understanding how data are represented before they can be processed by any digital system including a digital computer. there are two basic ways of representing the numerical values of the various physical quantities with which we constantly deal in our day-to-day lives. The arithmetic value that is used for representing the quantity and used in making calculations is defined as NUMBERS. A symbol like “4, 5, 6” which represents a number is known as a numeral.

Without numbers, counting things is not possible, date, time, money, etc. These numbers are also used for measurement and used for labeling. The properties of numbers make them helpful in performing arithmetic operations on them.  These numbers can be written in numeric forms and also in words.

For example, 3 is written as three in words, 35 is written as thirty-five in words, etc. Students can write the numbers from 1 to 100 in words to learn more. There are different types of numbers, which we can learn. They are whole and natural numbers, odd and even numbers, rational and irrational numbers, etc.

Types of Number Systems

Based on the base value and the number of allowed digits, number systems are of many types. The four common types of Number System are:

• Decimal Number System
• Binary Number System
• Octal Number System
• Hexadecimal Number System

1. Decimal Number System 

Number system with a base value of 10 is termed a Decimal number system. It uses 10 digits i.e. 0-9 for the creation of numbers. Here, each digit in the number is at a specific place with a place value of a product of different powers of 10. Here, the place value is termed from right to left as first place value called units, second to the left as Tens, so on Hundreds, Thousands, etc. Here, units have a place value of 100, tens have a place value of 101, hundreds as 102, thousands as 103, and so on. 

For example, 10264 has place values as,

(1 × 10⁴) + (0 × 10³) + (2 × 10²) + (6 × 10¹) + (4 × 10⁰)

= 1 × 10000 + 0 × 1000 + 2 × 100 + 6 × 10 + 4 × 1

= 10000 + 0 + 200 + 60 + 4

= 10264

2. Binary Number System 

Number System with base value 2 is termed as Binary number system. It uses 2 digits i.e. 0 and 1 for the creation of numbers. The numbers formed using these two digits are termed Binary Numbers. The binary number system is very useful in electronic devices and computer systems because it can be easily performed using just two states ON and OFF i.e. 0 and 1.

Decimal Numbers 0-9 are represented in binary as: 0, 1, 10, 11, 100, 101, 110, 111, 1000, and 1001

For example, 14 can be written as 1110, 19 can be written as 10011, 50 can be written as 110010.

Example of 19 in the binary system

Here 19 can be written as 10011

3. Octal Number System 

Octal Number System is one in which the base value is 8. It uses 8 digits i.e. 0-7 for the creation of Octal Numbers. Octal Numbers can be converted to Decimal values by multiplying each digit with the place value and then adding the result. Here the place values are 80, 81, and 82. Octal Numbers are useful for the representation of UTF8 Numbers. Example,

(135)₁₀ can be written as (207)₈

(215)₁₀ can be written as (327)₈

4. Hexadecimal Number System 

Number System with base value 16 is termed as Hexadecimal Number System. It uses 16 digits for the creation of its numbers. Digits from 0-9 are taken like the digits in the decimal number system but the digits from 10-15 are represented as A-F i.e. 10 is represented as A, 11 as B, 12 as C, 13 as D, 14 as E, and 15 as F. Hexadecimal Numbers are useful for handling memory address locations.The hexadecimal number system provides a condensed way of representing large binary numbers stored and processed. Examples,

(255)₁₀  can be written as (FF)₁₆

(1096)₁₀  can be written as (448)₁₆

(4090)₁₀  can be written as (FFA)₁₆

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