GATE CS 2023 Q11 — Combinational Circuits

To find the functional equivalence of the given circuit, let us analyze the behavior of a $2$-to-$1$ multiplexer (MUX).

The output $Y$ of a standard $2$-to-$1$ MUX with select input $S$ and data inputs $I_0$ and $I_1$ is given by the Boolean expression:

In the given circuit:

• The select line $S$ acts as an Enable ($E$) control signal.
• The data input $I_1$ is connected to an external input $D$.
• The data input $I_0$ is connected to the feedback loop from the output $Y$ (representing the current state $Q$).

Substituting these connections into the MUX equation, we get the next-state equation for the output $Q_{\text{next}}$:

Let us analyze the behavior based on the value of the enable signal $E$:

1. When $E = 1$: $$Q_{\text{next}} = (0 \cdot Q) + (1 \cdot D) = D$$ The output directly follows the input $D$ (transparent mode).
2. When $E = 0$: $$Q_{\text{next}} = (1 \cdot Q) + (0 \cdot D) = Q$$ The output retains its previous state (hold mode).

This level-sensitive behavior (where the output follows the input when the control signal is active and holds its state when inactive) is the characteristic behavior of a D Latch.

Therefore, the circuit is functionally equivalent to a D Latch.