EC 1201DIGITAL ELECTRONICS
A. Jawahar,
Assistant Professor, ECE Dept.
SSN College of Engineering
Phone: 044 32909855 275 (Extn : 359)
91-9444067484 (cellphone)
Email: jawahara@ssn.edu.in
Overview
Understanding flip flop state:
Stored values inside flip flops
Clocked sequential circuits:
Contain flip flops
Representations of state:
State equations
State table
State diagram
Finite state machines
Mealy machine
Moore machine
Flip Flop State
Behavior of clocked sequential circuit can be
determined from inputs, outputs and FF state
y(t) = x(t)Q
1
(t)Q
0
(t)
Q
0
(t+1) = D
0
(t) = x(t)Q
1
(t)
Q
1
(t+1) = D
1
(t) = x(t) + Q
0
(t)
x
Q
1
Q
0
D
Q
Q
D
Q
Q
y
Q
0
Q
1
D
0
D
1
Clk
Output and State Equations
Next state dependent on previous state.
State equations
Output equation
y(t) = x(t)Q
1
(t)Q
0
(t)
Q
0
(t+1) = D
0
(t) = x(t)Q
1
(t)
Q
1
(t+1) = D
1
(t) = x(t) + Q
0
(t)
x
Q
1
Q
0
D
Q
Q
D
Q
Q
y
Q
0
Q
1
D
0
D
1
Clk
State Table
Sequence of outputs, inputs, and flip flop states
enumerated in state table
Present state indicates current value of flip flops
Next state indicates state after next rising clock
edge
Output is output value on current clock edge
0 0
0 1
1 0
1 1
Present
State
Next State
x=0 x=1
00 10 0 0
10 10 0 0
00 11 0 0
10 11 0 1
Q
1
(t) Q
0
(t) Q
1
(t+1) Q
0
(t+1)
x=0 x=1
Output
State Table
State Table
All possible input combinations enumerated
All possible state combinations enumerated
Separate columns for each output value.
Sometimes easier to designate a symbol for each
state.
Present
State
Next State
x=0 x=1
s
0
s
2
0 0
s
2
s
2
0 0
s
0
s
3
0 0
s
2
s
3
0 1
x=0 x=1
Output
s
0
s
1
s
2
s
3
Let:
s
0
=00
s
1
=01
s
2
=10
s
3
=11
State Diagram
Circles indicate current state
Arrows point to next state
For x/y, x is input and y is output
0 0
0 1
1 0
1 1
Present
State
Next State
x=0 x=1
00 10 0 0
10 10 0 0
00 11 0 0
10 11 0 1
x=0 x=1
Output
01 10 00
0/0
1/0
0/0
1/0
0/0
0/0
11
1/1
1/0
State Diagram
s
1
s
2
s
0
0/0
1/0
0/0
1/0
0/0
0/0
s
3
1/1
1/0
Each state has two arrows leaving
One for x = 0 and one for x = 1
Unlimited arrows can enter a state
Note use of state names in this example
Easier to identify
Flip Flop Input Equations
D
Q0
= xQ
1
D
Q1
= x + Q
0
Boolean expressions which indicate the input to
the flip flops.
Format implies type of flop used
x
Q
1
Q
0
D
Q
Q
D
Q
Q
y
Q
0
Q
1
D
0
D
1
Clk
Analysis with D Flip-Flops
Identify flip flop input equations
Identify output equation
Note: this example
has no output
Mealy Machine
Comb.
Logic
X(t)
Q(t+1)
Q(t)
Y(t)
clk
present
state
present
input
next
state
Comb.
Logic
Output based on state and present input
Flip
Flops
Moore Machine
Comb.
Logic
X(t)
Q(t+1)
Q(t)
Y(t)
clk
present
state
present
input
next
state
Comb.
Logic
Output based on state only
Flip
Flops
Outputs
Output
Logic
Combina-
tional
Combina-
tional
Logic
Input
Memory
Element
Inputs
Mealy Model
Outputs
Output
Logic
Combina-
tional
Combina-
tional
Logic
Input
Memory
Element
Inputs
Moore Model
Mealy versus Moore
State Diagram with One Input & One Mealy Output
Mano text focuses on Mealy machines
State transitions are shown as a function of
inputs and current outputs.
S1
S2
S3
S4
1/0
1/0 1/0
1/1
Input(s)/Output(s) shown
in transition
0/0
0/0 e.g. 1
0/0
0/0
State Diagram with One Input & a Moore Output
Moore machine: outputs only depend on the
current state
Outputs cannot change during a clock pulse if the
input variables change
Moore Machines usually have more states.
No direct path from inputs to outputs
Can be more reliable
Clocked Synchronous State-machine Analysis next class
Given the circuit diagram of a state machine:
1 Analyze the combinational logic to determine flip-flop input
(excitation) equations: D
i
= F
i
(Q, inputs)
The input to each flip-flop is based upon current state and circuit inputs.
2 Substitute excitation equations into flip-flop characteristic
equations, giving transition equations: Q
i
(t+1) = H
i
( D
i
)
3 From the circuit, find output equations: Z = G (Q, inputs)
The outputs are based upon the current state and possibly the inputs.
4 Construct a state transition/output table from the transition and
output equations:
Similar to truth table.
Present state on the left side.
Outputs and next state for each input value on the right side.
Provide meaningful names for the states in state table, if possible.
5 Draw the state diagram which is the graphical representation of
state table.
Summary
Flip flops contain state information
State can be represented in several forms:
State equations
State table
State diagram
Possible to convert between these forms
Circuits with state can take on a finite set of values
Finite state machine
Two types of machines
Mealy machine
Moore machine
