Computer Science 210 Computer Organization

1. Computer Science 210Computer Organization Sequential Circuits Finite State Machines

2. State Machine • A type of sequential circuit • Combinational logic + storage • Remembers state • Changes output and state based in inputs and current state State Machine Inputs Outputs Combinational Logic Circuit Storage Elements

3. 4 1 8 4 30 25 5 20 10 15 Combinational or Sequential? Combinational Success depends only onthe values, not the order in which they are set. Sequential Success depends onthe sequence of values (e.g, R-13, L-22, R-3).

4. 30 25 5 20 10 15 States of Sequential Lock Our 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. R-13, L-22, R-3

5. 30 25 5 20 10 15 State Diagram R-13, L-22, R-3 Shows states and actions that cause transitions between states

6. 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

7. The Clock “1” “0” One Cycle time The clock cycle triggers a transition between states

8. 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?

9. Solution: Master/Slave Flipflop A 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.

10. Storage • Each flipflop stores one state bit • Number of flipflops is determined by number of states • Sequential lock had four states, so two bits

11. Blinking Traffic Sign • A 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) 3 4 1 5 2 DANGERMOVERIGHT

12. Traffic Light State Diagram Switch on Switch off State bit S1 State bit S0 Outputs Transition on each clock cycle.

13. Truth Tables Outputs (depend only on state: S1S0) Next State: S1’S0’(depend on state and input) Switch Lights 1 and 2 Lights 3 and 4 Light 5 Whenever In=0, next state is 00.

14. Traffic Light Circuit Master-slaveflipflop