Number System is a method of representing numbers on the number line with the help of a set of Symbols and rules. These symbols range from 0-9 and are termed as digits. Let’s learn about the number system in detail, including its types, and conversion.
Number system in Maths is a writing system for expressing numbers. It is a mathematical notation for representing numbers of a given set, consistently using digits or other symbols. It allows us to perform arithmetic operations like addition, subtraction, multiplication, and division.
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:
1. Decimal Number SystemNumber system with base value 10 is termed as 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 place value a product of different powers of 10. 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 has the place value as 100, tens has the place value as 101, hundreds as 102, thousands as 103, and so on.
For example: 10285 has place values as
(1 × 104) + (0 × 103) + (2 × 102) + (8 × 101) + (5 × 100)
1 × 10000 + 0 × 1000 + 2 × 100 + 8 × 10 + 5 × 1
10000 + 0 + 200 + 80 + 5
10285
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 as Binary Numbers.
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
Examples:14 can be written as 1110
19 can be written as 10011
50 can be written as 110010
Octal Number System is one in which the base value is 8. It uses 8 digits i.e. 0-7 for creation of Octal Numbers. Octal Numbers can be converted to Decimal value 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
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.
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
Practise it: put your number sense to work in one of our free math games.