Using a 4-bit adder to perform subtraction What modification enables a standard 4-bit adder to subtract one operand from another (A – B) using two’s complement?

Introduction / Context:
Many arithmetic logic designs reuse adders for subtraction by leveraging two’s complement. Understanding how to adapt hardware adders avoids extra circuitry and simplifies ALU design.

Given Data / Assumptions:

• Target operation: A – B implemented with an adder.
• Adder: 4-bit binary adder with a carry-in (Cin).
• We can optionally complement inputs and set Cin as needed.

Concept / Approach:
Two’s complement method for A – B computes A + (two’s complement of B). The two’s complement of B equals B' + 1, where B' is the bitwise inversion of B. Hardware trick: invert each B input and set Cin = 1; the adder then performs A + B' + 1 = A – B.

Step-by-Step Solution:
Two’s complement: (-B) = B' + 1.Hardware: feed B through inverters to form B'.Set Cin = 1 to add the +1 term automatically.The adder computes A + B' + 1 = A – B.

Verification / Alternative check:
Example: A = 0110 (6), B = 0011 (3). Invert B → 1100, set Cin = 1: 0110 + 1100 + 0001 = 0011 with Cout ignored, which is decimal 3 = 6 – 3.

Why Other Options Are Wrong:
Inverting the output: does not add the +1 term and does not create two’s complement of B.Inverting the carry-in: Cin is a single bit; inverting it alone cannot implement subtraction.Grounding B inputs: forces B = 0, yielding A – 0 only.Tying carry-out to carry-in: risks oscillation and does not realize two’s complement subtraction.

Common Pitfalls:
Forgetting to set Cin = 1 in addition to inverting B; both steps are required in practical circuits (many MCUs or ALUs implement this via XOR gates on B and an add-with-carry instruction).

Final Answer:
inverting the B inputs