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.
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 :
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 is done similar to multiplication of two decimal numbers.
Simple example :
Division is done same as two decimal numbers.
Simple example :
Binary to decimal conversion
Steps:
Example:
Binary to octal conversion
Steps:
Example:
Binary to hexadecimal conversion
Steps:
Example:
Every communication between the electronic componets inside the computer system takes place using binary number system.