# Complement of binary numbers

Digital computers use complement for simplifying the subtraction operation. The binary numbers is subtracted by using 1’s complements method allows subtraction only by addition.

**Types **

There are two types of complements

- 1’s complements
- 2’s complements

**1’s** complements:

When we change the binary number in 1’s complements than we change all 1’s to 0’s and all 0’s to 1’s.

**Method:**

When subtracting the smaller number from larger number, we follow

Remove the carry and add it to the result this process is known as end around carry

#### Example of 1’s complement:

Subtracting 10102 from 11112

**1’s complement method:**

**Direct method:**

**Steps: **

When we subtracting a larger number from smaller number one by one 1’s complements method involve the steps

There is no carry the answer is the 1’s complements of the result and is opposite in sign.

#### 2’s complements:

When we change the binary numbers in 2’s complement we firstly change it in 1’s complements than add in 1 to its 1’s complements.

**Method: **

When subtracting the smaller number from larger number by using 2’s complements method, we follow

Neglect the carry there is always a carry in this case

#### 2’s Complements Example:

Subtract 10102 from 11112

**2’s complements method:**

**Direct method:**

** Step:**

# The carry is omit so the answer is 01012

# When subtracting the smaller number from larger number by using 2’s complements method, we follow

When the answer is true from, take the 2’s complements and change the sign.

#### Comparison between 1’s and 2’s complements:

** **

**1’s** complements

- Using inverter it can be easily obtain
- In which we use two operations
- For inversion operation it is used in logic manipulations

**2’s** complements

- firstly we change the binary number in 1’s complements than add 1 in it
- in which we use only one operation
- it is used only in arithmetic applications