Binary Arithmetic





You have to learn addition, subtraction, multiplication and division of binary number. In brain, you have to keep that in the arithmetic of binary number, carry is written in binary (2) just like as 10 is used in decimal system for carry.

 

 

Binary Arithmetic

Binary Arithmetic


 

  • Addition of Binary numbers: Follow the following formulae:
Addition of Binary Numbers

Addition of Binary Numbers


Example:

1010   first number

1001    second number

10011    Results

 

  • Subtraction of Binary Numbers: The subtraction of binary is more interesting, but less complex for novice students, but not fear, jump to complement methods when confusion takes place in the traditional methods of subtraction.

Example: 110-11 =011

The first step is to equalize digits placing zero to the left side and make columns. You take right most columns and solve 0-1. The carry 2 is taken and 1 is subtracted, result is written as 1.

Binary Subtraction

Binary Subtraction


Next step, come to second column from where you have to solve again 0-1. To solve it take carry 2 from left and subtract 1 and write result as 1.

Binary Subtraction

Binary Subtraction


Example: 1000-11=0101

Example of Binary Subtraction

Example of Binary Subtraction


Example:

1000-1 =111

1000-10=110

 

Complement method: If you get difficulty in subtraction, the complement method is very easy solution. The complement of 1 is 0 and vice versa. The computer computes all the arithmetic operation like as subtraction, multiplication, and division by the method of addition.

Example: Write complement of 0110 is 1001.

Procedure: Suppose you have a problem: 1000-1. It is some difficult for novice.

Step-1: Equalize digits adding 0 in the left side.

Example: 1000-0001

Step-2: Write complement of 0001 as 1110 and add.

Complement Method

Complement Method


Step-3: Add carry to the previous addition.

Complement Method

Complement Method


So, 1000-0001 = 0111

 

  • Multiplication of Binary Numbers: The multiplication of binary number is also like as decimal multiplication.

Example:

Multiplication

Multiplication



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