Two’s complement subtraction setup: To compute 43 − 15 in binary by addition, which 6-bit two’s-complement code should be added to 43 to represent “minus 15”?

Introduction / Context:
Digital systems perform subtraction by adding the two’s complement of the subtrahend. Selecting the correct two’s-complement pattern is crucial for correct results and for understanding how ALUs handle subtraction internally.

Given Data / Assumptions:

• Operation: 43 − 15.
• Assume 6-bit words (sufficient since 43 is 101011₂ and 15 is 001111₂).
• Task: choose the 6-bit two’s complement of 15 to add to 43.

Concept / Approach:
For two’s complement: –N = invert(all bits of N) + 1. Represent 15 in 6 bits, form its two’s complement, and identify the correct option.

Step-by-Step Solution:

Verification / Alternative check:
Perform the addition: 43 (101011) + 110001 = 1 011100 (ignore carry) = 011100 = 28, which equals 43 − 15, confirming the correctness.

Why Other Options Are Wrong:

• 110000: Missing the +1 step; this is one’s complement of 15, not two’s.
• 101011 / 011100: These are unrelated values (43 and 28, respectively), not the needed complement.

Common Pitfalls:
Forgetting to add 1 after inversion; using too few bits so that sign is lost; misreading leading zeros in fixed-width formats.

Final Answer:
110001