Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
State Machine
Another type of sequential circuit
• Combines combinational logic with storage
• “Remembers” state, and changes output (and state)
based on inputs and current state
3-2
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Combinational vs. Sequential
Two types of “combination” locks
30
4 1 8 4
25
5
20
10
15
Combinational
Success depends only on
the values, not the order in
which they are set.
Sequential
Success depends on
the sequence of values
(e.g, R-13, L-22, R-3).
3-3
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
State
The state of a system is a snapshot of
all the relevant elements of the system
at the moment the snapshot is taken.
Examples:
• The state of a basketball game can be represented by
the scoreboard.
Number of points, time remaining, possession, etc.
• The state of a tic-tac-toe game can be represented by
the placement of X’s and O’s on the board.
3-4
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
State of Sequential Lock
Our lock example has four different states,
labelled A-D:
A: The lock is not open,
and no relevant operations have been performed.
B: The lock is not open,
and the user has completed the R-13 operation.
C: The lock is not open,
and the user has completed R-13, followed by L-22.
D: The lock is open.
(user has completed R-13, L-22 and then R-3)
3-5
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
State Diagram
Shows states and
actions that cause a transition between states.
3-6
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Definition of a Finite State Machine
•
•
•
•
•
A set of input events
A set of output events
A set of states
A function that maps states and input to output
A function that maps states and inputs to states (which is
called a state transition function)
• Must be complete
• A description of the initial state
A finite state machine is one that has a limited or finite number
of possible states.
3-7
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Example 2: A Door Combination Lock
entry code is the 4-bit sequence “0110”
Partial
Complete
3-8
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Example 3: Odd Parity Checker
3-9
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Why Finite State Machines (FSMs)
•
A FSM is simple and intuitive way of describing a
system which has discrete dynamics (State Transition
Diagrams).
•
An FSM is an “abstract machine.” That means that we
use a mathematical description of the machine to
reason about it without actually building it.
•
A FSM can be directly and unambiguously converted
into a digital electronic circuits. 
3-10
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Step 1: Form the State Transition Table (STT)
(NS)
3-11
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Step 2: Code STT in numbers
(NS)
(NS)

3-12
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Step 3: Implement STT
3-13
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Step 3a: Next State Logic for 1 D-Latch
Inputs
Output
NS= (~PS S) + (PS ~S)
3-14
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Step 3b: Output Logic
Inputs
Output
R= PS
3-15
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Step 4: Implement Circuit
3-16
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
The Clock
Frequently, a clock circuit triggers transition from
one state to the next.
“1”
“0”
One
Cycle
time
At the beginning of each clock cycle,
state machine makes a transition,
based on the current state and the external inputs.
• Not always required. In lock example, the input itself triggers a transition.
3-17
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Master-Slave Flipflop
A pair of gated D-latches,
to isolate next state from current
state.
PS
During 1st phase (clock=1),
previously-computed state
becomes current state and is
sent to the logic circuit.
PS
NS
During 2nd phase (clock=0),
next state, computed by
logic circuit, is stored in
Latch A.
3-18