Assignment #3 3.1 Implement the following Boolean function with a multiplexer: F(w,x ,y, z) = ? (0, 1, 2, 4, 5, 7, 8, 9, 12, 13) 3.2 Design a combinational circuit that can detect if a number is prime. The circuit should have four inputs w, x, y, z, and one output p, where p is 1 when the number represented by wxyz is prime, i.e, 2, 3, 5, 7, 11, and 13. 3.3 Design a combinational circuit with three input, I3, I2, I1, and two outputs, O1, O0, that behaves as follows. The outputs indicate the highest index of the inputs that is 1. For example, if I3 is 0, I2 is 1, I1 is 1, then O1, O0 would be 10 (i.e., I2 is the highest input set to 1) (a) Specify the function by filling out a complete truth table. (b) Develop the minimized implementation using the K-map method. (c) Develop an implementation using two 4-to-1-line multiplexers. (d) Develop an implementation using a 3-to-8-line decoder. 4.1 The connections of a JK flip-flop are as shown in the diagram below. If the flip-flop is initially in state 1, what state is the flip-flop in after two clock pulses are received? 1
4.2 Given the following sequential circuit: (a) Determine the input equations for two flip-flops. (b) Construct the state table of the circuit. (c) Draw a state diagram for the circuit. 4.3 Show how to build a JK flip-flop using a T flip-flop with combinational logic. (Hint: Express T in terms of J, K, and Q to find a solution) 4.4 Design a sequential circuit with two JK flip-flops, and one input x. When x = 0, the state of the circuit remains the same. When x = 1, the circuit goes through the state transitions from 00 to 01 to 11 to 10 back to 00, and repeats. 2 J Q K Q’ CLK
3