GATE CS 2002 Q2-1 — Combinational Circuits

Based on the logic circuit diagram, the system consists of two gates:

1. An AND gate with inputs $f_1$ and $f_2$.
2. An OR gate with inputs being the output of the AND gate and $f_3$, producing the final output $f$.

Thus, the Boolean expression for the output $f$ is:

We are given the minterm representations of the functions:

• $f_1(x,y,z) = \Sigma (0,1,3,5)$
• $f_2(x,y,z) = \Sigma (6,7)$
• $f(x,y,z) = \Sigma (1,4,5)$

First, let's find the output of the AND gate, which corresponds to the intersection ($\cap$) of the minterms of $f_1$ and $f_2$:

Now, substitute this result back into the expression for $f$:

Therefore, we have:

This matches Option A.