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Binary Number System


We have studied in previous point that binary number system consists of two numbers 0's and 1's, now we are going to learn binary related arithmetic operations, complements and conversions.

Binary addition :

Performing addition of two binary number is same as addition of two decimal numbers i.e. add individual bits and propagate the carry.

Rules of binary addition

Augend Addend Sum Carry Result
0 0 0 0 0
0 1 1 0 1
1 0 1 0 1
1 1 0 1 10

Simple example :

Binary substraction :

Is same as performing substraction of two decimal numbers.

Rules of binary substraction

Minuend Subtrahend Difference Borrow
0 0 0 0
0 1 1 1
1 0 1 0
1 1 0 0

Simple example :

Binary multiplication :

Binary multiplication is done similar to multiplication of two decimal numbers.

Simple example :

Binary division :

Division is done same as two decimal numbers.

Simple example :


One's complement:

Two's complement:


Binary to all conversions:

Binary to decimal conversion

Steps:

Example:

Binary to octal conversion

Steps:

Example:

Binary to hexadecimal conversion

Steps:

Example:


Tip Box

Every communication between the electronic componets inside the computer system takes place using binary number system.


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