Find the `2's` complement of the following numbers?
(a) 111111 (b)000000 (c) 101010 (d) 001001

Answer

To find the 2's complement of the given binary numbers, we will follow these steps for each number:

1. **Find the 1's complement**: This involves flipping all the bits (changing 0s to 1s and 1s to 0s).
2. **Add 1 to the 1's complement**: This will give us the 2's complement.

Let's apply these steps to each part of the question.

### (a) Find the 2's complement of 111111

1. **1's complement**:
- Flip the bits: 111111 → 000000
2. **Add 1**:
- 000000 + 000001 = 000001

**Final answer for (a)**: 000001

### (b) Find the 2's complement of 000000

1. **1's complement**:
- Flip the bits: 000000 → 111111
2. **Add 1**:
- 111111 + 000001 = 0000000 (carry is discarded)

**Final answer for (b)**: 000000

### (c) Find the 2's complement of 101010

1. **1's complement**:
- Flip the bits: 101010 → 010101
2. **Add 1**:
- 010101 + 000001 = 010110

**Final answer for (c)**: 010110

### (d) Find the 2's complement of 001001

1. **1's complement**:
- Flip the bits: 001001 → 110110
2. **Add 1**:
- 110110 + 000001 = 110111

**Final answer for (d)**: 110111

### Summary of Answers:
- (a) 000001
- (b) 000000
- (c) 010110
- (d) 110111