Binary arithmetic: What is the 1's complement (bitwise inversion) of the two-bit binary number 10?

Introduction / Context:In digital logic, the 1's complement of a binary value is obtained by flipping every bit: zeros become ones and ones become zeros. It is a foundational operation in binary arithmetic, checksums, and two's-complement negation steps.

Given Data / Assumptions:

• Number: '10' in binary, explicitly two bits long.
• Operation: 1's complement (bitwise NOT), not two's complement.

Concept / Approach:

Apply inversion to each bit independently. For a two-bit pattern, the left bit and right bit are processed the same way: 1 becomes 0, 0 becomes 1.

Step-by-Step Solution:

Verification / Alternative check:

Using logical NOT (~) at the bit level confirms: ~(10₂) = 01₂ when the width is fixed at two bits.

Why Other Options Are Wrong:

• 11: flips only the last bit incorrectly.
• 110: changes bit-width; not permitted for a two-bit representation.
• 10: unchanged; not a complement.
• None of the above: incorrect because '01' is correct.

Common Pitfalls:

• Confusing 1's complement with 2's complement (which adds 1 after inversion).
• Accidentally changing the number of bits during the operation.

Final Answer:

01.