Counting single-bit subtraction cases How many distinct basic one-bit binary subtraction operations (A − B, without borrow-in) are possible?

Introduction / Context:Binary subtraction at the single-bit level underpins subtractor design and the generation of borrow signals in arithmetic logic units.

Given Data / Assumptions:

• Single-bit operands A and B ∈ {0,1}.
• No borrow-in (Bin = 0).
• Outputs: difference bit D and borrow-out Bout.

Concept / Approach:With two binary inputs A and B, there are 2 × 2 = 4 input combinations. Each combination yields a defined (D, Bout).

Step-by-Step Solution:List cases: (A,B) = (0,0), (0,1), (1,0), (1,1).Compute D,Bout for each: 0−0→D=0,Bout=0; 0−1→D=1,Bout=1; 1−0→D=1,Bout=0; 1−1→D=0,Bout=0.Thus, there are four distinct basic operations.

Verification / Alternative check:Truth table of a one-bit subtractor confirms four rows.

Why Other Options Are Wrong:3, 2, 1: underestimate the number of input combinations.

Common Pitfalls:Accidentally including borrow-in changes the table size, but the question specifies basic operations without borrow-in.

Final Answer:4