Compute the 1's complement of a binary word Find the 1's complement (bitwise inversion) of the binary number 101010₂. Select the correct result.

Introduction / Context:Complements are foundational in digital arithmetic. The 1’s complement of a binary number is produced by flipping every bit: 1 becomes 0 and 0 becomes 1. This operation is used in some arithmetic schemes and in checksum calculations, so fluency with complements is essential.

Given Data / Assumptions:

• Original number: 101010₂ (six bits).
• 1’s complement means bitwise inversion only (no +1 as in 2’s complement).
• We preserve the bit-width.

Concept / Approach:Apply the transformation b_i → 1 − b_i to each bit. This is equivalent to XOR with 1 for every position. Perform it left to right or right to left—order does not matter as long as each bit is inverted once.

Step-by-Step Solution:

Verification / Alternative check:Use a quick mental check: the pattern 101010 becomes 010101, confirming that each position flipped.

Why Other Options Are Wrong:

Common Pitfalls:Confusing 1’s complement (invert) with 2’s complement (invert then add 1).

Final Answer:010101₂