Binary subtraction fundamentals: For the single-bit operation 0 − 0 in binary, what are the resulting difference and borrow?

Introduction / Context:Understanding one-bit subtraction is foundational for building half-subtractors and full-subtractors, and for interpreting multi-bit subtraction with borrows in arithmetic logic units.

Given Data / Assumptions:

• Operands: A = 0, B = 0.
• No incoming borrow from a less significant bit.
• Binary subtraction is performed bitwise.

Concept / Approach:For single-bit subtraction A − B with no borrow-in, the truth cases are simple: 0−0, 0−1, 1−0, and 1−1. The difference bit is the result in the current position; the borrow indicates that the next higher bit must be reduced by one.

Step-by-Step Solution:Compute 0 − 0: since the minuend equals the subtrahend, the difference is 0.No borrowing is required because we are not subtracting a larger bit from a smaller one.Hence, difference = 0 and borrow = 0.

Verification / Alternative check:Truth table for a half-subtractor confirms: A=0, B=0 → D=0, Borrow=0; A=0, B=1 → D=1, Borrow=1; A=1, B=0 → D=1, Borrow=0; A=1, B=1 → D=0, Borrow=0.

Why Other Options Are Wrong:Difference = 1 (options b and c) contradicts equal operands.Borrow = 1 (options c and d) is only needed when subtracting 1 from 0.

Common Pitfalls:Confusing “borrow” with “carry,” or assuming a default borrow-in of 1.

Final Answer:difference = 0 borrow = 0