Question

Design a system whose output goes high only after 8 consecutive 1's appear on the input; once the output goes high, it takes four consecutive 0's on the input to make the output go low again. You will use one switch as the input, and one button as the clock.

On a piece of paper, sketch an FSM diagram that solves the design problem. Make sure your FSM diagram meets the following requirements: - All states are properly specified. - Each state is labelled (inside the circle) with a descriptive name that indicates what the state is remembering. Each state is labelled (below the circle) with the output of the circuit

Assign a binary state code to each state of your FSM.

On a piece of paper, develop a truth table for the next state and output logic.

Answer 1

Given that the system output should go high only after 8 consecutive 1's appear at the input

And once the output goes high, it should take 4 consecutive 0's on the input to make the output go low again.

8 consecutive 1's indicates 8 states

4 consecutive 1's indicates 4 states.

So total number of states requred are 8 + 4 = 12 states

We need to assign these 12 states with a binary state code for each state.

A	0000
B	0001
C	0010
D	0011
E	0100
F	0101
G	0110
H	0111
I	1000
J	1001
K	1010
L	1011

As per the given condition the state diagram is as shown in the below image.

0/0 Co 000 90 0/0 olo 0 olo H ㅌ A) B C Vo VO G 170 이 10 10 (Vo Vo 601 yo 이 이 (100 0100 0000 0020 1000 0001 00 1001 0101 110) I 코 이 na VI

Let us draw the output table and for each of the input and also mention the state .

The truth table for the next state and output logic for the Above FSM diagram is as shown below

Present State	X (INPUT)	Next State	Y(OUTPUT)
A (0000) A (0000)	0 1	A B	0 0
B (0001) B (0001)	0 1	A C	0 0
C (0010) C (0010)	0 1	A D	0 0
D (0011) D (0011)	0 1	A E	0 0
E (0100) E (0100)	0 1	A F	0 0
F (0101) F (0101)	0 1	A G	0 0
G (0110) G (0110)	0 1	A H	0 0
H (0111) H (0111)	0 1	A I	0 1
I (1000) I (1000)	0 1	J I	1 1
J (1001) J (1001)	0 1	K I	1 1
K (1010) K (1010)	0 1	L I	1 1
L (1011) L (1011)	0 1	A I	0 1

In order to explain the above truth table let us do it by taking an example.

For example: if we take an input 01011111111010000

Present state	INPUT	NEXT STATE	OUTPUT
A	0	A	0
A	1	B	0
B	0	A	0
A	1	B	0
B	1	C	0
C	1	D	0
D	1	E	0
E	1	F	0
F	1	G	0
G	1	H	0
H	1	I	1
I	1	I	1
I	0	J	1
J	0	K	1
K	0	L	1
L	0	A	0

Here the output has shifted from 0 to1 after 8 consecutive 1's and reached state I.

Also the output has shifted from 1 to 0 after 4 consecutive 0's. and reached state A .

I hope the from the above example it is easy to understand the Problem.

If you are satisfied with the solution please give it a THUMBS UP!!!