Topic: Digital Circuits
For a binary half subtractor having two input A and B, the correct set of logical expressions for the outputs $D=(A-B)$ and X(borrow) are
- A. $D=AB+\overline{A}\overline{B}$, $X=\overline{A}B$
- B. $D=\overline{A}B+A\overline{B}$, $X=\overline{A}B$
- C. $D=\overline{A}B+A\overline{B}$, $X=A\overline{B}$
- D. $D=B+\overline{A}\overline{B}$, $X=A\overline{B}$
Answer: B. $D=\overline{A}B+A\overline{B}$, $X=\overline{A}B$
Explanation: For a half subtractor computing A minus B:
The Difference output $D$ is $1$ when the inputs are different, which is the XOR operation: $D = A \oplus B = \overline{A}B + A\overline{B}$.
The Borrow output $X$ is $1$ only when subtracting $1$ from $0$ (i.e., $A=0$ and $B=1$), so $X = \overline{A}B$.