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

Difficulty: Easy

Correct Answer: 01

Explanation:


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:

Write the original two-bit number: 1 0.Invert each bit: 1 → 0, 0 → 1.Concatenate the results to get 0 1, i.e., '01'.


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.

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