For the given logic gate circuit, which of the following is the correct truth table?

Solution

Physics sir · 2 steps

Write z as one Boolean expression, and the absorption law shrinks it to just n̅.

1. Read the circuit. Input n goes straight to the NAND gate and also into the OR gate with m. The OR output n + m is the second input of the NAND gate, so z = n · (n + m)̅.

   n · (n + m) = n + n m = n(1 + m) = n ⇒ z = n̅

   n	m	n + m	n · (n + m)	z
   0	0	0	0	1
   0	1	1	0	1
   1	1	1	1	0
   1	0	1	1	0

2. So. The output does not depend on m at all: z = 1 when n = 0 and z = 0 when n = 1. That matches option (a).

The idea to keep. For a gate circuit, write the output as one expression and simplify it before filling the table. Laws like A(A + B) = A often make one input drop out completely.

Answer from the NTA final answer key. Solution by PrepWiser.