Question

The values of \(Y\) and \(Z\) in the given logic circuit are

• A. \(Y=1,\quad Z=1\)
• B. \(Y=0,\quad Z=1\)
• C. \(Y=1,\quad Z=0\)
• D. \(Y=0,\quad Z=0\)

Hint:

In logic circuits, solve gate by gate from left to right. Remember: \[ \text{AND gives }1\text{ only when all inputs are }1 \] \[ \text{OR gives }1\text{ if at least one input is }1 \] NAND is the complement of AND

Answer 1

The Correct Option is A

Step 1: Identify the logic gate types and trace the circuit.
The circuit contains AND, OR, NAND and NOT gates. Based on the solution description, the circuit has two input paths that merge. We trace the signal from inputs to outputs.

Step 2: Evaluate the upper AND gate.
The inputs are 1 and 0. An AND gate gives output 1 only when BOTH inputs are 1.
\[ 1 \cdot 0 = 0 \] Output of upper AND gate: 0.

Step 3: Evaluate the lower OR gate.
The inputs are 0 and 1. An OR gate gives output 1 when AT LEAST ONE input is 1.
\[ 0 + 1 = 1 \] Output of lower OR gate: 1.

Step 4: Evaluate the middle OR gate (combining upper AND output and a signal).
Inputs to the middle OR gate are 0 (from AND) and 1.
\[ 0 + 1 = 1 \] Output: 1.

Step 5: Find Y from the NAND gate.
The NAND gate takes inputs 0 and 1. First compute AND: $0 \cdot 1 = 0$. NAND inverts this:
\[ Y = \overline{0 \cdot 1} = \overline{0} = 1 \]

Step 6: Find Z from the final OR gate.
The lower OR gate output (1) passes through a NOT gate: $\overline{1} = 0$. The final OR gate takes $Y = 1$ and 0:
\[ Z = 1 + 0 = 1 \] \[ \boxed{Y = 1,\; Z = 1} \]