Repair the subtraction rule: For 1-bit binary subtraction 0 − 1, the correct result is difference = 1 with a borrow-out of 1 (not 0). Evaluate the statement “difference = 1 borrow = 0.”

Introduction / Context:Single-bit subtraction cases underpin multi-bit subtractor design. Understanding the borrow behavior for each case prevents design and analysis mistakes in arithmetic circuits.

Given Data / Assumptions:

• We consider 1-bit subtraction with minuend M and subtrahend S, no initial borrow-in.
• Case examined: M = 0, S = 1.
• Difference bit D and borrow-out Bout follow standard rules.

Concept / Approach:If the minuend bit is smaller than the subtrahend bit, a borrow is required from the next higher bit position. For 0 − 1 at the LSB with no borrow-in, the difference is 1 (after borrowing 1 as 2 in binary) and the borrow-out is 1. Therefore, claiming borrow = 0 is incorrect.

Step-by-Step Solution:

Verification / Alternative check:Truth table for 1-bit subtraction confirms: M=0, S=1, Bin=0 ⇒ D=1, Bout=1. Hardware half-subtractor equations yield D = M ⊕ S, Bout = ~M * S (which evaluates to 1 for 0 − 1).

Why Other Options Are Wrong:

• Correct: Contradicts the established subtractor behavior.
• Ambiguous / Cannot be determined: The case is explicit and standard.

Common Pitfalls:Confusing borrow with carry, or forgetting that 0 − 1 requires borrowing even in the least significant position.

Final Answer:Incorrect