1. Design the state diagram and create the state table for a synchronous to detect the sequence 0101. The circuit has a single input, x, and a single output z. The output is logic-1 whenever the input sequence 0101 is detected, logic-0 otherwise. Note that overlapping sequences are allowed (that is: If the input is 01010101, the output is high on every 1 beginning with the second). Write the equations for the state variables and the output z. 2. Design the state diagram and create the state table for a synchronous modulo-3 counter (that is, one that continually counts in the sequence 0, 1, 2, 0, 1, 2, ...). Write the equations for the state variables. Note: In this case, the state variables can be used as the outputs.

Write the logic expression that represents the output of the following circuit as a function of its inputs. (Do not simplify your expression). OUT Use logic rules to simplify your expression. Show each step and state the law of logical equivalence that are applying at each step. Draw the circuit corresponding to your simplified expression.

The following circuit implements a state machine. Obtain its state table and state diagram. (You need to show all the steps). D Q CLK CLK reset reset

Q1: Let F1 = X.Y , F2 = AOB , F3 = F1+ F2 Implement the above Boolean expression with logic circuit . giving the ... truth table.

6) Draw the Mealy state diagram for a sequence detector that detects the sequence 0101 using a minimal number of states. The detector should also detect overlapping sequences. Design the circuit using D flip-flops. Draw the logic diagram. 7) Draw the Mealy state diagram for a sequence detector that detects the sequence 11001100 using a minimal number of states. The detector should also detect overlapping sequences.

Develop a simple program in C# that receives two binary inputs from the user (graphical or command line) and outputs the result of the selected gate operation. Gate operations that should be selectable are AND, OR, XOR.

Given the following logic circuit, a logic expression for the output function is: Z O F(x,y,z) = x.(z+y)+z.(z+y) OF(x,y,z) = (z+y).(x+z) O F(x,y,z) = x.z+x.y+z+z.y O F(x,y,z) = x.y+z O All of the above O None of the above F

Given the following logic function: F = x’y’z’ + xyz + xy’z + x’yz’ Simplify the logic function. Draw the logic diagram after simplification.

boolean expression: P = not((not(a.b) + c) + a.c)  (c) Show that P (the Boolean expression above) is equivalent to the Boolean expression Q = a · b · not(c) and draw the corresponding circuit.

1- In the following sequential circuit. There are 2 D FF (A and B), 2 inputs (x and y), and 1 output z The output and next-states equations are given A(t+1) = x'y + xà B(t+1) = x'B + xA z= B c- Draw the corresponding state diagram.