Question

$\text{Consider the circuit shown below:}$


$\text{then, which of the following statement is true}$

• A. $\text{When A = 1 and B = 1, Output X = 0 and Y = 1}$
• B. $\text{When A = 1 and B = 1, Output X = 0 and Y = 1}$
• C. $\text{When A = 0 and B = 1, Output X = 1 and Y = 1}$
• D. $\text{When A = 0 and B = 0, Output X = 1 and Y = 0}$

Answer 1

The correct option is C $\text{When A = 0 and B = 1, Output X = 1 and Y = 1}$

$X=\overline{B}(A+\overline{B})+\overline{A}(A+B)=A\overline{B}+\overline{A}B=A⨁BY=B\left(\overline{AB}\right)=B(\overline{A}+\overline{B})=\overline{A}B\text{The above circuit represents a half subractor constructed using only NAND gates.}\text{Thus the truth table can be written as}\begin{array}{cccc}\text{A}& \text{B}& \text{Difference (X)}& \text{Borrow(Y)}\\ 0& 0& 0& 0\\ \text{0}& 1& 1& 1\\ 1& 0& 1& 0\\ 1& 1& 0& 0\end{array}$