List of top Digital Logic Questions on Combinational and Sequential Circuits asked in GATE CS

Consider the following logic circuit diagram.

Consider a digital display system (DDS) shown in the figure that displays the contents of register X. A 16-bit code word is used to load a word in X, either from S or from R. S is a 1024-word memory segment and R is a 32-word register file. Based on the value of mode bit M, T selects an input word to load in X. P and Q interface with the corresponding bits in the code word to choose the addressed word. Which one of the following represents the functionality of P, Q, and T? \includegraphics[width=0.5\linewidth]{image40.png}

Which one of the following circuits implements the Boolean function given below?
\[ f(x,y,z) = m_0 + m_1 + m_3 + m_4 + m_5 + m_6, \] where $m_i$ is the $i^{\text{th}}$ minterm.

Suppose we want to design a synchronous circuit that processes a string of 0's and 1's. Given a string, it produces another string by replacing the first 1 in any subsequence of consecutive 1's by a 0. Consider the following example.
Input sequence: 00100011000011100
Output sequence: 00000001000001100
A Mealy Machine is a state machine where both the next state and the output are functions of the present state and the current input. The above mentioned circuit can be designed as a two-state Mealy machine. The states in the Mealy machine can be represented using Boolean values 0 and 1. We denote the current state, the next state, the next incoming bit, and the output bit of the Mealy machine by the variables $s$, $t$, $b$ and $y$ respectively. Assume the initial state of the Mealy machine is 0. What are the Boolean expressions corresponding to $t$ and $y$ in terms of $s$ and $b$?

Consider a 3-bit counter, designed using T flip-flops, as shown below. Assuming the initial state of the counter given by $PQR$ as $000$, what are the next three states?