# 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.

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**Addition of Binary numbers**: Follow the following formulae:

*Example:*

1010 first number

1001 second number

10011 Results

: 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.*Subtraction of Binary Numbers*

*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.

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.

*Example*: 1000-11=0101

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.

**Step-3**: Add carry to the previous addition.

So, 1000-0001 = 0111

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

*Example:*

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