The 1’s complement of binary 101010 is
A) 010110
B) 010101
C) 110111
D) 101011
The Correct Answer and Explanation is:
The correct answer is:
B) 010101
Explanation (300+ words):
To understand the 1’s complement of a binary number, it’s important to know what the term means and how it works.
What is 1’s Complement?
The 1’s complement of a binary number is formed by inverting each bit of the number. This means:
- Change every 1 to 0
- Change every 0 to 1
So, it’s a bit-wise inversion.
Step-by-Step Conversion:
We are given the binary number:
101010
Let’s break it down and flip each bit:
| Original Bit | Inverted Bit |
|---|---|
| 1 | 0 |
| 0 | 1 |
| 1 | 0 |
| 0 | 1 |
| 1 | 0 |
| 0 | 1 |
So, the 1’s complement is:
010101
This is answer B.
Why Use 1’s Complement?
1’s complement is used in some computing systems, especially older ones, for representing negative numbers. In such systems:
- A positive number is stored as it is in binary.
- A negative number is stored as the 1’s complement of its positive counterpart.
However, modern systems more commonly use 2’s complement, which is slightly different and avoids issues like having both a +0 and -0.
Important Notes:
- The length of the binary number must remain the same. You simply flip each bit.
- Do not add 1 (that would be 2’s complement).
- This technique is commonly used in digital electronics and computing.
Conclusion:
To get the 1’s complement of a binary number like 101010, just flip all the bits. This gives:
101010 → 010101
So the correct answer is:
B) 010101 ✅