Question

3. Implement a Mealy FSM to detect the "1100110” sequence with overlap. The output Y should be a 'l' only when the sequence has been detected and 'O' otherwise. Obtain the state transition diagram, state transition table, state assignment table, output table, next-state equations, and output equations for this FSM. Use SR flip-flops for state storage. Simplify the equations as much as possible using a K-map. Use don't cares as necessary. 4. Implement the sequence detector above using a Moore FSM.

Answer both parts please

Answer 1

3)

A Mealy FSM to detect the sequence " 1100110" with Overlap is implemented below.

Since the length of the sequence is equal to 7 then total number of states required is also equal to 7

The states are assigned with Alphabets

SINCE THERE ARE 7 STATES NUMBER OF BITS TO REPRESENT THE STATE IS EQUAL TO 3

STATE ASSIGNMENT TABLE:

STATES	BINARY VALUE
A	000
B	001
C	010
D	011
E	100
F	101
G	110

STATE TRANSITION DIAGRAM :

이이 이 이 10 olo ܘܐ ܘ 이 이 이어 ajo YO Vo 10이 CA 이이 01 00) 001 000 yo I/O 9 110 110

STATE TRANSITION TABLE:

From the below state transition table we can clearly see that the output becomes 1 when there is a transition from G to C.

It implies that the required sequence has been detected and due to the overlap of the sequence the next transition state is C. but not A.  

PRESENT STATE INPOT NEXT STATE OUTPUT o A 000 H OOO o А Ooo B 001 o HO B 001 A 000 O B I со (о 001 01 010 C o D oll o c 010 1 Co10 o D Ol o E 100 OU B 001 0 Ojo 100 A 000 F 101 o Alu olda 10o A 000 101 0 Ho Ho Hot R10 G lol o D 011 G Ilo G lio colo

TOTAL NUMBER OF STATES =7

AND WE KNOW THAT

$2^{N}\geq 7$

So, N= 3.

Hence 3 number of flipflops are required.

4)

A Moore FSM to detect the sequence " 1100110" with Overlap is implemented below.

Since the length of the sequence is equal to 7 then total number of states required is equal to 8

The states are assigned with Alphabets

SINCE THERE ARE 8 STATES NUMBER OF BITS TO REPRESENT THE STATE IS EQUAL TO 3

STATE ASSIGNMENT TABLE:

STATES	BINARY VALUE
A	000
B	001
C	010
D	011
E	100
F	101
G	110
H	111

STATE TRANSITION DIAGRAM

F 빙 D 0 소 I A B 0 0 1 0 보 I H 0

STATE TRANSITION MATRIX:

From the below state transition table we can clearly see that the output becomes 1 when the Circuit enters the H state.

It implies that the required sequence has been detected and due to the overlap of the sequence the next transition state is E if input is 0 and B if input is 1 but not A.  

PRESENT INPUT OUTPUT STATE A 000 NEXT STATE H OOO B A 000 001 0 B ool A 000 Horlo B C 010 ool O10 o olo o C D Oll с 010 colo D ll с 100 D ou B 00) o olo С 100 A 000 Hlo Ho Ho Ho E F 101 100 10) A 000 D D G to 101 001- 110 Hill o G 011 1 colo H lll E 100 001 H II) 1 Q B

TOTAL NUMBER OF STATES =8

AND WE KNOW THAT

$2^{N}\geq 8$

So, N= 3.

Hence 3 number of flipflops are required.