Find the 2s complement of binary number `(10101)_2` ?

Answer

To find the 2's complement of the binary number \( (10101)_2 \), we will follow these steps:

### Step 1: Find the 1's Complement
To find the 1's complement of a binary number, we convert all 1s to 0s and all 0s to 1s.

- Given binary number: \( 10101 \)
- Convert 1 to 0 and 0 to 1:
- 1 → 0
- 0 → 1
- 1 → 0
- 0 → 1
- 1 → 0

So, the 1's complement of \( 10101 \) is \( 01010 \).

### Step 2: Add 1 to the 1's Complement
Now, we will add 1 to the 1's complement obtained in Step 1.

- 1's complement: \( 01010 \)
- Add 1:
```
01010
+ 1
--------
01011
```

### Result
The result of the addition is \( 01011 \).

Thus, the 2's complement of the binary number \( (10101)_2 \) is \( (01011)_2 \).

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