Binary Number System||Bit System

 

Binary Number System – Definition, Conversion, Examples

 

Number  System||Numeral System

The number system or the numeral system is the system of naming or representing numbers in various formats. We know that a number is a numerical value that helps to count or measure objects and it helps in performing various mathematical calculations. There are different types of number systems in Maths but we categories number system in four major category- decimal number system, binary number system, octal number system, and hexadecimal number system.

Binary Number System||Bit System

 

  A binary number system with base-2 is one of the four types of number systems. Binary number system played historical role in development of computer history.

 0 and 1 are two digits represents a  binary system .  In the word “binary”, “bi” means “two”.  The base-2 numeral system is used to represent binary numbers. For example, (1010)₂ is a binary number where 2 is the radix. Each digit in the binary number system is called to be a “bit”. 

 

Role of binary system in Computer development

 

This number system is widely used in computers. Binary number are used in digital electronic circuitry using logic gates. Since computer only understand binary information (0’s and 1’s). Any  inputs given to a computer are decoded by it into a series of 0’s or 1’s before being processed . It is simple to convert a decimal number into a binary number and vice-versa. The notations for decimal numbers and binary numbers are different. For example, a decimal is represented as (15)₁₀ where 10 is the base of the decimal number, and the corresponding binary number is represented as (1111)₂ where 2 is the base of a binary number

     All the coding and languages(C, C++, Java , any other languages or any other coding platform ) in computers use binary digits 0 and 1 to write a program

 

 

		Reminder which represent binary number from bottom to top
2	8
2	4	0
2	2	0
2	1	0
	0	1
Binary conversion method
Decimal Number	Binary Number	Decimal Number	Binary Number
1	001	11	1011
2	010	12	1100
3	011	13	1101
4	100	14	1110
5	101	15	1111
6	110	16	10000
7	111	17	10001
8	1000	18	10010
9	1001	19	10011
10	1010	20	10100
Binary decimal number table

 

What is number System

 

Number System||Numeral System

The number system or the numeral system is the system of naming or representing numbers in various formats. We know that a number is a numerical value that helps to count or measure objects and it helps in performing various mathematical calculations. There are different types of number systems in Maths but we categories number system in four major category- decimal number system, binary number system, octal number system, and hexadecimal number system.

Definition of Number System.

A number system is defined as a system of writing to express 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 number systems in mathematics. 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)

The decimal number system has a base of 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..Every position shows a particular power of the base (10).

Example:

The decimal number 1873 consists of the digit 3 in the unit position, 7 in the tens place, 8 in the hundreds position, and 1 in the thousands place whose value can be written as: Base 10 Number System

ð  (1×10³) + (8×10²) + (7×10¹) + (3×10⁰)

ð  (1×1000) + (8×100) + (7×10) + (3×1)       :X⁰ =1

ð  1000 + 800 + 70 + 3

ð  1873

Binary Number System (Base 2 )

The number with base 2 is also known as the binary number system. 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, 010101 is a binary number.

We can convert any system into binary and vice versa. Base 2 Number System

Example :

Write (15)₁₀ as a binary number.

Solution:

2	15
2	7	1
2	3	1
	1	1

 

 

Base 2 Number System Example

∴ (15)₁₀ = 1111₂

Octal Number System (Base 8 Number System)

The number with base 8 is known as the Octal Number System and it uses numbers from 0 to 7 to represent Octal Numbers System. Octal numbers are commonly used in computer applications. Converting an octal number to decimal is the same as decimal conversion and is explained below using an example.

Example: Convert 1873₈ into decimal.

Solution:

1873₈ = 1 × 8³ + 8 × 8² + 7 × 8¹ + 3 × 8⁰

= 1 × 512 +8 × 64 + 7 × 8 + 3 × 1

= 512 +512 + 56+ 3

= 1083₁₀

Hexadecimal Number System (Base 16 Number System)

The number with base 16 is known as the Hexadecimal Number System and it uses numbers from 0 to 9 then alphabet from A to F  to represent Octal Numbers 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 the decimal system, i.e. from 0 to 9. Then, the numbers are represented using the alphabet A(10), B(11), C(12),D(13),E(14) and  F(15).

Example: Convert 5B4E₁₆ into decimal.

Solution:

5B4E₁₆ = 5 × 16³ + 11 × 16² + 4 × 16¹ + 14 × 16⁰                :: B=11 and E=14

= 5 × 4096 +11 × 256 + 4 × 16 +14 × 1

= 20480 +2816 + 64+ 14

= 23274 ₁₀

FAQs on Number System

What is Number System?

The number system is simply a system to represent or express numbers.

 

What are Types of Number System ?

There are various types of number systems 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)