Circuit Design of a Sequence Detector

This post illustrates the circuit design of Sequence Detector for the pattern “1101”. State Machine diagram for the same Sequence Detector has been shown below. Click here to realize how we reach to the following state transition diagram.

Click here to learn the step by step procedure of “How to synthesize a state machine / How to boil down a state machine to the circuit level”.

Now as we have the state machine with us, the next step is to encode the states. For 4 states:

State     Encoding

S0            00

S1            01

S2            10

S3            11

We need only 2 flipflops to represent these 4 states. For this example we will be using T Flipflips to design the circuit.

Let’s draw the state transition table using the Excitation table of T flipflop

PS Q2(t)  Q1(t)	X Input	NS Q2(t+1) Q1(t+1)	Excite (T) T2  T1	O Output
0        0	0	0           0	0   0	0
0        0	1	0           1	0   1	0
0        1	0	1           0	1   1	0
0        1	1	0           1	0   0	0
1        0	0	0           0	1   0	0
1        0	1	1           1	0   1	0
1        1	0	1           0	0   1	0
1        1	1	0           1	1   0	1

Now to realize the combinational logic we have to find out the Boolean expression for 3 output variables (of the above table) T2, T1 and O in terms of 3 input variable Q2(t), Q1(t) and X.

T2	T1
Y	Boolean Expressions
	T2 = Q2′(t)Q1(t)X’ + Q2(t)Q1′(t)X’ +         Q2(t)Q1(t)X T1 = Q1(t)X’ + Q1′(t)X = Q1(t) ⊕ X O = Q2(t)Q1(t)X

Let’s draw the respective circuit diagram for the given Sequence Detector.