Question

The following figure is the combination of logic gates. The inputs are A and B. The output is C. Which one of the following choices gives the correct matching?

• A. OUTPUT A
• B. OUTPUT B
• C. OUTPUT C
• D. OUTPUT D
• E. OUTPUT E

Hint:

To solve complex logic circuits, simplify Boolean expressions at each stage using laws like $A + AB = A$. This often reduces a massive looking circuit to a single simple gate.

Answer 1

The Correct Option is D

Concept: A logic gate circuit is analyzed by determining the Boolean expression for the output based on the input states.
• AND gate output is 1 only if all inputs are 1.
• OR gate output is 1 if at least one input is 1.
• Gates with tied inputs (e.g., A and A) act as a buffer or simply pass the signal.

Step 1: {Analyze the first stage of the circuit.}
The top section has an AND gate with inputs $A$ and $B$, giving output $Y_1 = A \cdot B$. Below that, an AND gate with both inputs tied to $A$ gives $Y_2 = A \cdot A = A$. These feed into an OR gate, giving $Y_3 = (A \cdot B) + A = A(B + 1) = A$.

Step 2: {Analyze the bottom stage of the circuit.}
The third gate is an OR gate with inputs $B$ and $B$, giving $Y_4 = B + B = B$. The fourth gate is an AND gate with inputs $B$ and $A$, giving $Y_5 = B \cdot A$. These feed into an OR gate (as implied by the diagram's final AND input), resulting in $Y_6 = B + (B \cdot A) = B(1 + A) = B$.

Step 3: {Determine the final output C.}
The final gate is an AND gate with inputs $Y_3$ and $Y_6$. Substituting the simplified results: $$C = Y_3 \cdot Y_6 = A \cdot B$$ Final gate is a NAND gate (indicated by a small circle at the output), the expression would be $C = \overline{A \cdot B}$. Option (D): If $A=0, B=0$, then $A \cdot B = 0$, $\overline{0} = 1$. If $A=1, B=1$, then $A \cdot B = 1$, $\overline{1} = 0$. This matches table (D).