Question

SEQUENCE is 101

In Lab Procedure

1. Draw the state diagram of the state machine below and show it to the lab instructor.

2. Fill the state table.

3. Assign State numbers

4. Find simplified Expressions (State Equations) for the flip-flops

5. Draw the circuit diagram using NAND GATES ONLY for the state machine

STATE DIAGRAM::

STATE TABLE::

State Table Next State Qc Y DA DB Dc Present State QA Qв 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 3 0 1 0 0 4 0 1 0 1 5 0 0 6 0 1 7 0 0 0 8 0 0 1 9 0 0 10 0 11 0 0 12 1 0 13 1 0 14 15

Answer 1

State Diagram:

State table

Present State

Input

Next State

Flip flop inputs

Output

QA	QB	Y	QA+	QB+	DA	DB	X
0	0	0	0	0	0	0	0	0
0	0	1	0	1	0	1	0	1
0	1	0	1	0	1	0	0	2
0	1	1	0	1	0	1	0	3
1	0	0	0	0	0	0	0	4
1	0	1	0	1	0	1	1	5
1	1	x	x	x	x	x	x	6

x - don't care

For DA

QA\QB Y	00	01	11	10
0				1
1			x	x

Mapping 010 and 110 will give expression

$DA = QB\overline{Y}$

For DB

QA\QB Y	00	01	11	10
0		1	1
1		1	x	x

Mapping 001,011,101 and 111 will give DB = Y

For output

QA\QB Y	00	01	11	10
0
1		1	x	x

Mapping 101 and 111 will give output(X) = QA.Y

State Equations

$\mathbf{DA = QB\overline{Y}}$

DB = Y

X = QA.Y

Circuit Diagram

2 3 9 10 11 DA U7 U8 U9 SET U5 U6 Q CLK -- Output RESET D_FF DB SET Y D 0 CIK >CLK O RESET Ş D_FF Design1*
Checking the input sequence

Input	0	1	1	0	1	0	1	0	1	0	0	0	1	0	1	1	0	1	0
State	0	1	1	2	1	2	1	2	1	0	0	0	1	2	1	1	2	1	2
Output	0	0	0	0	1	0	1	0	1	0	0	0	0	0	1	0	0	1	0
Input (Cont)	0	1	1	0	1	0	1	0	1	0	0	0	1	0	1	1	0	1	0
State	0	1	1	2	1	2	1	2	1	0	0	0	1	2	1	1	2	1	2
Output	0	0	0	0	1	0	1	0	1	0	0	0	0	0	1	0	0	1	0

THANK YOU