Consider three 4-variable functions f_{1}, f_{2}, and f_{3}, which are expressed in sum-of-minterms as f_{1 }= $\sum$ (0, 2, 5, 8, 14), f_{2} = $\sum$ (2, 3, 6, 8, 14, 15), f_{3} = $\sum$ (2, 7, 11, 14) For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:
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 .
Consider the two cascaded 2-to-1 multiplexers as shown in the figure.
The minimal sum of products form of the output $X$ is
Consider the 4-to-1 multiplexer with two select lines S_{1} and S_{0} given below.
The minimal sum-of-products form of the Boolean expression for the output F of the multiplexer is
Let k= 2^{n}. A circuit is built by giving the output of an n-bit binary counter as input to an n-to-2^{n} bit decoder. This circuit is equivalent to a
The above synchronous sequential circuit built using JK flip flop is initialized with Q_{2}Q_{1}Q_{0}=000.THe state sequence for these circuit for next 3 clock cycle is
In the following truth table, V = 1 if and only if the input is valid.
What function does the truth table represent?
The truth table
represents the Boolean function
Consider the following circuit involving three D-type flip-flop used ina certain type of counter configuration.
if at some instance prior to the occurance of the clock edge P ,Q,and R have value 0, 1 and 0 respectively, what shall be the val ue of PQR after the clock edge?
If all the flip-flop were reset to 0 at power on ,what is the total number of distinct outputs (states) represented by PQR generated by the counter?
The Boolean expression for the output f of the multiplexer shown below is
What is the Boolean expression for the output f of the combinational logic circuit of NOR gates given below?
In the sequential circuit shown below, if the initial value of the output Q_{1}Q_{0} is 00, what are the next four values of Q_{1}Q_{0}?
How many 3-to-8 line decoders with an enable input are needed to construct a 6-to-64 line decoder without using any other logic gates?
Suppose only one multiplexer and one inverter are allowed to be used to implement any Boolean function of n variables. What is the minimum size of the multiplexer needed?
The control signal functions of a 4-bit binary counter are given below (where X is “don’t care”):
The counter is connected as follows:
Assume that the counter and gate delays are negligible. If the counter starts at 0, then it cycles through the following sequence: