Class Notes (810,860)
CSC258H1 (46)
Lecture

# feb06ce.docx

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School
University of Toronto St. George
Department
Computer Science
Course
CSC258H1
Professor
Steve Engels
Semester
Winter

Description
 Example #3: Counters – moved to feb04ce o Let Green = 00, Yellow = 01, Red = 10  Finite State Machines o State table o From theory courses, mainly used to describe the grammars of a State Prev. F F Write State Next F ’ F ’ 1 0 1 0 language, or to model sequence data Green 0 0 0 Green 0 0  A finite state machine is an abstract model that captures the Green 0 0 1 Yellow 0 1 operation of a sequential circuit Yellow 0 1 0 Yellow 0 1  Finite State Machines are models for an actual circuit Yellow 0 1 1 Red 1 0 design Red 1 0 0 Red 1 0  These states represent internal states of the circuit which Red 1 0 1 Green 0 0 are stored in the flip-flop values  FSM design steps o A FSM is define (in general) as: o 1. Draw state diagram o 2. Derive state table from state diagram  A finite set of states  A finite set of transitions between states triggered by inputs to o 3. Assign flip-flop configuration to each state the state machine  Number of flip-flops needed is ceiling2log (# of states))  Output values that are associated with each state or transition o 4. Redraw state table with flip-flop values (depending on the machine) o 5. Derive combinational circuit for output and for each flip-flop input  State and end states for the state machine  FSM Example #4: Recognizer  FSM Example #1: Tickle Me Elmo o Recognize a sequence of input values, and raise a signal if that input o Toy reacts differently each time it is squeezed has been seen o Questions to ask: o Example: Three high values in a row  Understood to mean that the input has been high for three  What are the inputs?  What are the states of this machine? rising clock edges  How do you change from one state to the next  Assumes a single input X and a single output Z o 1. State diagram  In this case, the states are labeled with the input values that have been seen up to now  Transitions between states are indicated by the values on the transition arrows o Usually FSM has more than one input and will trigger a transition based on certain input values but not others o Also might have input values that don’t cause a trandition, but keep the circuit in the same state  FSM Example #2: Alarm Clock o Internal state description  Starts in a neutral state, until timer signal goes off  Clock moves to alarm state  Alarm state continues until  A snooze button is pushed (move to snooze state) o 2. State table  Alarm is turned off (move to neutral state)  Make sure that the state table lists all the states in the state  Timer goes off again (move to neutral state) diagram, and all the possible inputs that can occur at that state  In snooze state, clock returns to alarm state when the timer State Prev. EN State Next signal goes off again 000 0 000  FSM Example #3: Traffic Light 000 1 001 001 0 010 001 1 011 010 0 100 010 1 101 011 0 110 011 1 111 100
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