UNIT 1 : Modeling
Module 1.4 : Modeling Sequential circuits
TOPIC : Finite State Machine(FSM)
and Flow Tables
FSM : Introduction
A finite state machine (FSM) is a
model of behavior composed of a finite
number of states, transitions between
those states, and actions
 Any Circuit with Memory is a Finite State
Machine
 Even computers can be viewed as huge
FSMs

Designing FSM
Defining states : Total states that system
can take.
 Defining transitions between states:
Logic behind going from one state to
another.
 Optimization / minimization :
Optimizing a FSM means finding the
machine with the minimum number of
states that performs the same function.

FSM in digital circuits

In digital circuits FSM can be made using
two types of elements :
◦ Sequential : Any storage element such as
Registers which will store the state of System.
◦ Combinational : 1) How the states are
changing from one to another. 2) How the
output is calculated.

FSM are of two types :
◦ Moore FSM
◦ Mealy FSM
Moore FSM

Output only depend on the present state.
0
1
0
1
S0 / 0
NOTE:
S0/0 = State/output
S1 / 0
1
0
In state S2 output = 1, since
10 sequence is detected
Moore FSM for “10” sequence detector
S2 / 1
Mealy FSM

Output Is a Function of a Present State and
Inputs
0/0
1/0
S0
reset
1/0
S1
0/1
Mealy FSM for “10” sequence detector

Mealy always have less number of state than
Moore.
HDL code for Moore FSM
IF(reset = ‘1’)
Moore_state <= S0;
ELSIF (clock = ‘1’ AND clock’event) THEN
CASE (Moore_state)
S0 :
IF (input = ‘1’) Moore_state <= S1;
Else Moore_state <= S0;
S1:
S2:
If (input == 0) Moore_state = S2;
Else Moore_state = S1;
If (input = ‘0’) Moore_state <= S0;
Else
Moore_state <= S1;
End Case;
example: A simple vending machine
Here is how the control is supposed to work. The vending machine delivers
a package of gum after it has received 15 cents in coins. The machine has a single
coin slot that accepts nickels and dimes, one coin at a time. A mechanical sensor
indicates to the control whether a dime or a nickel has been inserted into the coin slo
The controller’s output causes a single package of gum to be released down a chute
to the customer.
One further specification: We will design our machine so it does not give
change. A customer who pays with two dimes is out 5 cents!
Coin
Sensor
Reset
Vending
Machine
FSM
Open
Gum
Release
Mechanism
CLK
Vending Machine block diagram
States:
0C
5C
10C
15C
8
— The figure below show the Moore and Mealy machine state transition diagrams.
Reset / 0
Reset
( N D  Reset)/0
0 cent
[0]
Reset
ND
D
( N D  Reset)/0
Reset /
0
N
5 cent
[0]
D
N
10 cent
[0]
N+D
15 cent
[1]
Moore machine
0 cent
N D /0
N/0
5 cent
D/0
D/1
N/0
ND
10 cent
N D /0
N+D/1
15 cent
Mealy machine
Moore and Mealy machine state diagrams for the vending machine FSM
9
Flow Tables
FSM can be represented in a tabular form
which is known as Flow Table.
 In a flow table the states are named by
letter symbols.

Input
Present
state
X1
X2
X3
X4
S0
S1,0
S3,0
S3,0
S0,1
S2
S1,0
S2,0
S3,0
S0,0
S3
S2,0
S2,0
S2,0
S0,0
S4
S3,0
S3,0
S3,0
S0,1
S0,1 = next state, output
Flow Table for Vendor machine
Example