Consider the synchronous sequential circuit in the below figure.

(a) Draw a state diagram, which is implemented by the circuit. Use the following names for the states corresponding to the values of flip-flops as given below.

(b) Given that the initial state of the circuit is S₄, identify the set of states, which are not reachable.

Design a synchronous counter to go through the following states:

  1, 4, 2, 3, 1, 4, 2, 3, 1, 4,........... 

The following arrangement of master-slave flip flops

has the initial state of P, Q as 0, 1 (respectively). After three clock cycles the output state P, Q is (respectively),

A sequential circuit takes an input stream of 0’s and 1’s and produces an output stream of 0’s and 1’s. Initially it replicates the input on its output until two consecutive 0’s are encountered on the input. From then onward, it produces an output stream, which is the bit-wise complement of input stream until it encounters two consecutive 1’s, whereupon the process repeats. An example of input and output stream is shown below.

The input stream: 101100 01001011 0 11
The desired output: 101100 10110100 0 11 

J-K master-slave flip-flops are to be used to design the circuit.
(a) Give the state transition diagram.
(b) Give the minimized sum-of-product expression for J and K inputs of one of its state flip-flops.

Consider the circuit given below with initial state Q₀ = 1, Q₁ = Q₂ = 0. The state of the circuit is given by the value 4Q₂ + 2Q₁ + Q₀

Which one of the following is the correct state sequence of the circuit?

Consider the following circuit with initial state Q₀ = Q₁ = 0. The D Flip-flops are positive edged triggered and have set up times 20 nanosecond and hold times 0.

Consider the following timing diagrams of X and C; the clock period of C <= 40 nanosecond. Which one is the correct plot of Y?

A 1-input, 2-output synchronous sequential circuit behaves as follows:

Let z_k, n_k denote the number of 0's and 1's respectively in initial k bits of the input (z_k + n_k = k). The circuit outputs 00 until one of the following conditions holds.

•   zk - nk = 2. In this case, the output at the k-th and all subsequent clock ticks is 10.
•   nk - zk = 2. In this case, the output at the k-th and all subsequent clock ticks is 01. 

What is the minimum number of states required in the state transition graph of the above circuit?

Start and stop bits do not contain an ‘information’ but are used in serial communication for

Choose the correct alternatives (more than one may be correct) and write the corresponding letters only: Advantage of synchronous sequential circuits over asynchronous ones is:

The circuit shown below implements a 2-input NOR gate using two 2-4 MUX (control signal 1 selects the upper input). What are the values of signals x, y and z?

Which of the following input sequences will always generate a 1 at the output Z at the end of the third cycle?

A line L in a circuit is said to have a stuck-at-0 fault if the line permanently has a logic value 0. Similarly a line L in a circuit is said to have a stuck-at-1 fault if the line permanently has a logic value 1. A circuit is said to have a multiple stuck-at fault if one or more lines have stuck at faults. The total number of distinct multiple stuck-at faults possible in a circuit with N lines is

How many pulses are needed to change the contents of a 8-bit up counter from 10101100 to 00100111 (rightmost bit is the LSB)?

Which of the following input sequences for a cross-coupled R-S flip-flop realized with two NAND gates may lead to an oscillation?

Consider the following state diagram and its realization by a JK flip flop The combinational circuit generates J and K in terms of x, y and Q. The Boolean expressions for J and K are:

The above circuit produces the output sequence:

Consider the partial implementation of a 2-bit counter using T flip-flops following the sequence 0-2-3-1-0, as shown below

To complete the circuit, the input X should be

In an SR latch made by cross-coupling two NAND gates, if both S and R inputs are set to 0, then it will result in

The minimum number of JK flip-flops required to construct a synchronous counter with the count sequence (0, 0, 1, 1, 2, 2, 3, 3, 0, 0,……) is ___________.

A positive edge-triggered D flip-flop is connected to a positive edge-triggered JK flipflop as follows. The Q output of the D flip-flop is connected to both the J and K inputs of the JK flip-flop, while the Q output of the JK flip-flop is connected to the input of the D flip-flop. Initially, the output of the D flip-flop is set to logic one and the output of the JK flip-flop is cleared. Which one of the following is the bit sequence (including the initial state) generated at the Q output of the JK flip-flop when the flip-flops are connected to a free-running common clock? Assume that J = K = 1 is the toggle mode and J = K = 0 is the state-holding mode of the JK flip-flop. Both the flip-flops have non-zero propagation delays.

Consider a 4-bit Johnson counter with an initial value of 0000. The counting sequence of this counter is

We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then repeats. The minimum number of J-K flip-flops required to implement this counter is __________.