Question

To get output 1 at R, for the given logic gate circuit the input values must be

• A. x = 0, y = 0
• B. x = 1, y = 0
• C. x = 0, y = 1
• D. x = 1, y = 1

Hint:

Read the circuit: \(P = \bar X + Y\), \(Q = \overline{X\cdot\bar Y}\), and the last gate is a NOR (OR with a bubble).

Answer 1

The Correct Option is B

From the figure: X goes through a NOT gate to the upper OR gate, whose other input is Y, so \(P = \bar X + Y\).
X goes directly to the NAND gate and Y goes through a NOT gate to its other input, so \(Q = \overline{X\cdot\bar Y}\).
The last gate is a NOR gate: \(R = \overline{P+Q}\). R = 1 needs \(P=0\) and \(Q=0\).
\(P=0\) needs \(\bar X=0\) and \(Y=0\), so \(X=1,\ Y=0\). Then \(Q = \overline{1\cdot1} = 0\), as required.
Check the others: (0,0): \(P=1\); (0,1): \(P=1\); (1,1): \(P=1\), so R = 0 in all of them.
Answer: (2) x = 1, y = 0