Find the 1s complement of binary number `(10101001)_2` ?

Explanation

To find the 1's complement of the binary number \( (10101001)_2 \), we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of 1's Complement**:
The 1's complement of a binary number is obtained by flipping all bits in the number. This means changing every 1 to a 0 and every 0 to a 1.

2. **Write Down the Given Binary Number**:
The binary number provided is \( 10101001 \).

3. **Flip Each Bit**:
- The first bit is 1, so it becomes 0.
- The second bit is 0, so it becomes 1.
- The third bit is 1, so it becomes 0.
- The fourth bit is 0, so it becomes 1.
- The fifth bit is 1, so it becomes 0.
- The sixth bit is 0, so it becomes 1.
- The seventh bit is 0, so it becomes 1.
- The eighth bit is 1, so it becomes 0.

4. **Combine the Flipped Bits**:
After flipping all the bits, we get the new binary number:
- 0 (from 1)
- 1 (from 0)
- 0 (from 1)
- 1 (from 0)
- 0 (from 1)
- 1 (from 0)
- 1 (from 0)
- 0 (from 1)

This results in the binary number \( 01010110 \).

5. **Final Answer**:
The 1's complement of the binary number \( (10101001)_2 \) is \( (01010110)_2 \).