What is Binary Number System Full Details

Binary Number System

What is Binary Number System:- Before telling this, I would like to ask in which language do you give instruction to the computer. Does the computer understand that instruction in the same language? Probably, your answer is no. Why and how are you thinking like this? Let us understand it with an example.

Suppose, you want to send a file from computer to pen drive, then to send we click on the option of copy or send. So will the computer understand that instruction directly? The answer is, no, the computer will first convert that instruction into binary, then it will understand and execute that language.

Let us know what is Binary Number System

(What is Binary Number System)

Whenever we give instruction to the computer, the instruction given to the computer gets converted into the binary number system, because, the computer understands only the binary number system.

Binary Number System is also called Binary Number System in Hindi language. The word ‘Bi’ in binary and ‘Bi’ in the word binary means, two.

Binary number system has only two digits, ‘0’ and ‘1’. Where, ‘0’ means switch off, and ‘1’ means switch on.

Because, there are only two digits in the binary number system. Therefore, its base or base or radix is ​​’2′.

‘0’ or ‘1’ means single digit ‘0’ and ‘1’ is also called bit.

Hope you have understood what is Binary Number System? Next, we will learn how to convert the binary number system to another number system (eg-decimal number system, octal number system, hexadecimal number system).

Before this we read about Number System Conversion. It is important that you have knowledge about Decimal Number System, Octal Number System and Hexadecimal Number System.

How to convert any Binary Number to Decimal Number. Before that let us understand what is LSB (Least Significant Bit) and MSB (Most Significant Bit)?

The lowest bit in a series of numbers is called LSB. for example,

The highest bit in a series of numbers is called MSB.

Topics

How to convert binary number to decimal.
(How to Convert a Binary Number to Decimal Number)
How to convert binary number to octal?
(How to Convert a Binary Number to Octal)
How to convert binary number to hexadecimal?
(How to Convert Binary to Hexadecimal Number System)

How to convert binary number to decimal

(How to Convert a Binary Number to Decimal Number)

Let’s start with an example,

(10110)2 is a binary number. First of all, start writing their positional value from the right hand side.

1 0 1 1 0

4 3 2 1 0 ——— positional value

24 23 22 21 20

(10110)2 = 0 × 20 + 1 × 21 + 1 × 22 + 0 × 23 + 1 × 24

= 0 + 2 + 4 + 0 + 16

= (22)10

How to convert binary number to octal?

(How to Convert a Binary Number to Octal)

To convert any binary number to octal, read the table given below carefully,

In which way we convert a binary number to octal, we understand it with an example, (100101011)2 is a binary number. From the right-hand side, the number will be made into a group of three. sorts of,

100 101 011

Write their corresponding number from the above table. like-

(100)2 is written as 4 in octal. (101)2 to 5 and (011)2 to 3. So, the octal number is (100 101 011)2 = (453)8

Note: By the way, it is difficult to remember the table. For this you can remember the 421-code. With the help of this 421-code, you can convert any octal number to binary or binary number to octal.

We all know that there are total 8 digits (0 to 7) in octal number system. So if you add the 421-code (4 + 2 + 1), the total value will be 7. Let us understand this with an example,

(3) 8 Convert the octal number to binary.

Now think that where you will write ‘1’ in 421-code so that their addition 3 comes. Write ‘1’ below 2 and 1, right. The rest will write ‘0’ below the second number. sorts of,

4 2 1

0 1 1

Now you can easily convert any octal number to binary and binary number to octal with the help of 421-code.

How to convert binary number to hexadecimal?

(How to Convert Binary to Hexadecimal Number System)

We know that hexadecimal number consists of 0 to 15 (16-digit) digits. Read the table given below,

To convert any binary number to hexadecimal, either you remember the above table or convert binary number to hexadecimal or hexadecimal number to binary with the help of 8421-code.

If you add the 8421-code (8+4+2+1), they add up to 15.

Let us understand this with an example how we can convert any hexadecimal number into binary using 8421-code.

Convert hexadecimal number (1AC)16 to binary

Now I would like to ask you people what is the meaning of A, A means 10.

In 8421-code, under which digit should we place ‘1’ so that their addition ’10’ comes. Exactly, adding 8 and 2 gives an addition ’10’, so put ‘1’ under 8 and 2 and ‘0’ under the rest of the digit (4 and 1). sorts of,

8 4 2 1

(1 0 1 0)2

Similarly, C represents digit 12. Which will write (1010)2 in binary and 01 in binary as (0001).

(1AC)16 = (0001 1010 1100)2

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