Demonstrate that this device has no illegal state, i.e. that there is no stable

Question

Demonstrate that this device has no illegal state, i.e. that there is no stable state in which Q = Q Fill out a truth table for the device, showing the next state Q(t+1) for all possible combinations of A, B. and the present state Q (t) . Summarize the behavior by showing a compact truth table with only three rows. Based on the analysis presented in earlier parts, describe the function of this sequential logic device. Is it level-sensitive or edge-triggered? What are the functions of the inputs? What type of device is it?

Explanation / Answer

1) assume A= 0    then output of mux = Q     ,output of NAND gate 1   =( Q' .Q')'= Q

                                                                      output of NAND gate 2 = (Q.Q)'= Q'

    assume A=1   then output of MUX = B            output of NAND gate 1   = (B' .Q')'=B+Q

                                                                          output of NAND gate 2= (B.Q)'=B'+Q'

so no illegle state present in circuit

2)    Q(t+1)= A'Q+A(B+Q)

3)

Reduced Truth table =

4) above circuit is level triggred

A B Q Q(t+1)= A(B+Q)+A'Q 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1

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