Question

Two 4-bit binary numbers \(A = 1101\) and \(B = 1010\) are given in the input logic circuit. Find the output \(Y\).

• A. \(1000\)
• B. \(1101\)
• C. \(0010\)
• D. \(0111\)

Answer 1

The Correct Option is B

Concept:
From the circuit: \begin{itemize} \item Input \(B\) first passes through a NOT gate giving \(\overline{B}\). \item The output then enters a NAND gate with \(A\). \end{itemize} Thus, \[ Y = \overline{A \cdot \overline{B}} \] Using De Morgan’s theorem: \[ Y = \overline{A} + B \] Step 1: Write the given binary numbers. \[ A = 1101 \] \[ B = 1010 \] Step 2: Find complement of \(B\). \[ \overline{B} = 0101 \] Step 3: Apply the Boolean expression. \[ Y = A + \overline{B} \] Performing OR operation: \[ \begin{array}{cccc} A & = & 1 & 1 & 0 & 1
\overline{B} & = & 0 & 1 & 0 & 1
\hline Y & = & 1 & 1 & 0 & 1 \end{array} \] \[ Y = 1101 \]