Computer Science 210Computer Organization

Sequential Circuits

Finite State Machines

State Machine

• A type of sequential circuit– Combinational logic + storage– Remembers state– Changes output and state based in inputs and

current state State Machine

CombinationalLogic Circuit

StorageElements

Inputs Outputs

Combinational or Sequential?

4 1 8 4

30

15

5

1020

25

CombinationalSuccess depends only onthe values, not the order in which they are set.

SequentialSuccess depends onthe sequence of values(e.g, R-13, L-22, R-3).

States of Sequential LockOur lock example has four different states,labeled 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.

30

15

5

1020

25

R-13, L-22, R-3

State Diagram

Shows states andactions that causetransitions betweenstates

30

15

5

1020

25

R-13, L-22, R-3

Finite State Machine (FSM)

• A finite number of states

• A finite number of inputs

• A finite number of outputs

• A finite number of state transitions

• Actions that specify output values

The Clock

“1”

“0”

timeOneCycle

The clock cycle triggers a transition between states

Problem

• Memory circuits (latches) maintain the states

• Current state must be sent from latch to a combinational circuit, which uses it to compute the next state

• Next state is fed back as input to latch

• Isn’t this circular?

Solution: Master/Slave FlipflopA pair of gated D-latches, to isolate next state from current state.

During 1st phase (clock=1),previously-computed statebecomes current state and issent to the logic circuit.

During 2nd phase (clock=0),next state, computed bylogic circuit, is stored inLatch A.

Storage

• Each flipflop stores one state bit

• Number of flipflops is determined by number of states

• Sequential lock had four states, so two bits

Blinking Traffic SignA blinking traffic sign

• No lights on

• 1 & 2 on

• 1, 2, 3, & 4 on

• 1, 2, 3, 4, & 5 on

• (repeat as long as switchis turned on)

DANGERMOVERIGHT

1

2

3

4

5

Traffic Light State Diagram

State bit S1 State bit S0

Switch onSwitch off

Outputs

Transition on each clock cycle.

Truth TablesOutputs(depend only on state: S1S0)

S1 S0 Z Y X

0 0 0 0 0

0 1 1 0 0

1 0 1 1 0

1 1 1 1 1

Lights 1 and 2

Lights 3 and 4

Light 5

Next State: S1’S0’(depend on state and input)

In S1 S0 S1’ S0’

0 X X 0 0

1 0 0 0 1

1 0 1 1 0

1 1 0 1 1

1 1 1 0 0

Switch

Whenever In=0, next state is 00.

Traffic Light Circuit

Master-slaveflipflop