Overview Finite State Machines Sequential circuits with inputs

Overview • Finite State Machines - Sequential circuits with inputs and outputs • State Diagrams - An abstraction tool to visualize and analyze sequential circuits

Combinational vs. Sequential Logic • Two types of “combination” locks 25 4 1 8 4 Combinational Success depends only on the values, not the order in which they are set. 20 30 15 5 10 Sequential Success depends on the sequence of values (e. g, R-13, L-22, R-3).

State Machine • A type of sequential circuit – Combines combinational logic with storage – “Remembers” state, and changes output (and state) based on inputs and current state State Machine Inputs Combinational Logic Circuit Storage Elements Outputs

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.

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.

State Diagram • Shows states and actions that cause a transition between states.

Finite State Machine • A description of a system with the following components: 1. 2. 3. 4. 5. A finite number of states A finite number of external inputs A finite number of external outputs An explicit specification of all state transitions An explicit specification of what determines each external output value • Often described by a state diagram. - The set of all possible states. - Inputs that trigger state transitions. - Outputs associated with each state (or with each transition).

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 (Synchronous). – Not always required. In lock example, the input itself triggers a transition (Asynchronous).

Implementing a Finite State Machine • Combinational logic – Determine outputs at each state. – Determine next state. • Storage elements – Maintain state representation. State Machine Inputs Clock Combinational Logic Circuit Storage Elements Outputs

Storage • Each master-slave flipflop stores one state bit. • The number of storage elements (flipflops) needed is determined by the number of states (and the representation of each state). • Examples: – Sequential lock • Four states – two bits – Basketball scoreboard • 7 bits for each score digit, 5 bits for minutes, 6 bits for seconds, 1 bit for possession arrow, 1 bit for half, …

Complete Example – Traffic Sign • Design a “blinking” traffic sign which exhibits this behavior: State 1) No lights on State 2) 1 & 2 on 3 4 State 3) 1, 2, 3, & 4 on 1 5 State 4) 1, 2, 3, 4, & 5 on 2 State 1) No lights on . DANGER. MOVE. RIGHT ( - Repeat as long as operate switch is turned on. - The system is in state 1 when the operate switch is off)

Traffic Sign State Diagram Switch on Switch off State bit S 1 State bit S 0 Transition on each clock cycle. Outputs

Traffic Sign Truth Tables Outputs (depend only on state: S 1 S 0) Lights 1 and 2 Switch Lights 3 and 4 In S 1 0 X 1 0 S 0 X 0 1 S 1 0 0 1 S 0 0 1 1 0 1 0 Light 5 S 1 0 0 1 S 0 0 1 0 Z 0 1 1 Y 0 0 1 X 0 0 0 1 1 1 Next State: S 1’ S 0’ (depend on state and input) 1 1 Whenever In=0, next state is 00.

Traffic Sign Combinational Logic Master-slave flipflop

Lab Project 1 – Traffic Signal (Due 10/29/07) Part 1: • Clearly explain a design – doesn’t have to be the one we did • Show the timing diagrams for the design implementation Part 2: • Implement your design on the Logic. Works 5 Simulator • Capture the timing diagrams from the Simulator for your report Part 3: (with ONE partner) • Build a circuit(s) in the Laboratory • Capture the oscilloscope traces for your report Part 4: • Document your project in a report written to a professional audience of your peers – Title Page, Abstract, Problem Description, Design, Data, Conclusions (include descriptions of problems and learning), and References) Have fun, explore, and don’t be afraid to be creative !