**Note**: The** 1`s complement** and the **2`s complement** of a binary number are important because they permit the representation of negative numbers.

**∴ Finding the 1`s complement:-**

The **1`s complement** of a binary number is found by changing all **1s** to** 0s** and all **0s** to** 1s**.

→ **How to find 1`s complement of binary number.**

∴ **1`s complement using NOT gate.**

Q). Find the 1`s complement of (10110)_{2}solution:-1`s complements = 01001 |

**Finding the 2`s complement**

The** 2`s complement** of a binary number is found by adding 1 to the LSB of the 1`s complement.

∴ **2`s complement = (1`s complement) + 1**

→ **How find 2`s complement of binary number**?

∴ **Alternative way to find direct 2`s complement**

- Start at the right with the LSB and write the bits as they are up to and including the first 1.
- Yake the 1`s complement of the remaining bits

**In the above solution**, we should write the same binary digits from right to left until we found 1, after that change the remaining bits into 1`s complement as shown above.

**→ Subtraction using 1`s complement**

• **Step 1:-** Take 1`s complement of subtrahend

• **Step 2:-** Add 1`s complement of subtrahend with minuend

**• Step 3:-** If got a carry, add the carry to its LSB. Else take 1’s complement of the result and put negative sign

**Subtracting using 2`s complement**

Step 1. Take 2`s complement of subtrahend

Step 2. Add 2`s complement of subtrahend with minuend

Step 3. If there is no carry , the result is negative and take the 2`s complement of above result and place negative sign in the final result.