Question

Create a state machine that outputs a high signal every time the string ‘001’ is detected. Use only four states in your state machine, and two JK flip-flops in your circuit design. As an example, ‘1101000010100011101’ should output a high signal two times.

Answer 1

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Answer 2

To design a finite state machine (FSM) that outputs a high signal upon detecting the sequence '001' using four states and two JK flip-flops, follow these steps:

1. Define the States:

• State S0: Initial state, no bits detected.

• State S1: '0' detected.

• State S2: '00' detected.

• State S3: '001' detected; output high.

2. State Transition Diagram:

• S0: On input '0' → transition to S1; on input '1' → stay in S0.

• S1: On input '0' → transition to S2; on input '1' → return to S0.

• S2: On input '0' → stay in S2; on input '1' → transition to S3.

• S3: On input '0' → transition to S1; on input '1' → stay in S0.

3. State Encoding:

With two JK flip-flops (Q1 and Q0), four states can be encoded as:

• S0: Q1Q0 = 00

• S1: Q1Q0 = 01

• S2: Q1Q0 = 10

• S3: Q1Q0 = 11

4. Transition Table:

Current State (Q1Q0)	Input (X)	Next State (Q1+Q0+)	Output (Z)
00 (S0)	0	01 (S1)	0
00 (S0)	1	00 (S0)	0
01 (S1)	0	10 (S2)	0
01 (S1)	1	00 (S0)	0
10 (S2)	0	10 (S2)	0
10 (S2)	1	11 (S3)	0
11 (S3)	0	01 (S1)	1
11 (S3)	1	00 (S0)	1

5. JK Flip-Flop Input Equations:

For JK flip-flops, the next state equations are:

• Q1+ = J1 * ~Q1 + ~K1 * Q1

• Q0+ = J0 * ~Q0 + ~K0 * Q0

Using Karnaugh maps (K-maps) to simplify, derive the equations for J and K inputs based on the transition table.

6. Output Logic:

The output Z is high (1) only in state S3:

• Z = Q1 * Q0

7. Circuit Implementation:

• Inputs: X (serial input)

• Outputs: Z (sequence detected)

• Flip-Flops: Two JK flip-flops for Q1 and Q0