Question

5. A circuit must detect a 01 sequence. The sequence sets z= 1,which is reset only by a 00 sequence. For all other cases, z = 0. Overlap is allowed in the sense that the second bit of the reset sequence “00” can be counted as the first bit of the next set sequence “01.” For example, for input sequence x as follows, the corresponding output sequence z would be:

x = 010100100

z = 011110110

For this circuit:

A) Use the JK flopflops to implement the circuit (2 flipflop are enough). Assign Q1Q0= 00 to state A, Q1Q0= 01, 10, and 11 to the states considered in their alphabetical order. Present the state table by representing the states in terms of the Q1Q0 values.

B) From the output transition table for JK flipflops, obtain the table showing for each state and input combination, the required J and K values that will cause the transitions shown in the table in 5(A).

C) Design using Karnaugh maps the 4 combinational circuits required to feed into the inputs of the 2 JK flipflops. Draw the final circuit (including function for z) for the sequence detection.

Answer 1

Its a Moore Machine.

SO S3 SI 1 S2

Excitation Table of JK Flip Flop and State Table is shown below:

Excitation Table of JK Flip Flop:

PRESENT STATE	NEXT STATE	INPUT
Q	Q+	J	K
0	0	0	X
0	1	1	X
1	0	X	1
1	1	X	0

State Table:

PRESENT STATE		INPUT	NEXT STATE		OUTPUT	JK FLIP FLOP INPUTs
Q1	Q0	X	Q1+	Q0+	Z	J1	K1	J0	K0
0	0	0	0	1	0	0	X	1	X
0	0	1	0	0	0	0	X	0	X
0	1	0	0	1	0	0	X	X	0
0	1	1	1	0	0	1	X	X	1
1	0	0	1	1	1	X	0	1	X
1	0	1	1	0	1	X	0	0	X
1	1	0	0	1	1	X	1	X	0
1	1	1	1	0	1	X	0	X	1

Karnaugh Map Simplification:

0 ㄧㄧㄨㄧㄨㄧ凶| x Ko=X

INPUT X J Q X1 Q1 Keno J Q Q0