EE101Lecture20

# EE101Lecture20 - Introduction to Digital Logic Lecture 20:...

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© Mark Redekopp, All rights reserved State Machine Review State Diagrams 1. States 2. Transition Conditions 3. Outputs State Machine 1. State Memory => FF‟s n- FF‟s => 2 n states 2. Next State Logic (NSL) combinational logic logic for FF inputs 3. Output Function Logic (OFL) MOORE: f(state) MEALY: f(state + inputs) SM NSL OFL D Q Q D Q Q Q 0 Q 1 D 0 D 1 X CLK F (Input) (Next State) (Current State) (Output) State Diagram for “101” Sequence Detector X=1 S101 S10 S1 Sinit X=0 X=1 X=0 X=1 F=1 X=1 X=0 X=0 On Reset (power on) F=0 F=0 F=0 State Machines require sequential logic to remember the current state (w/ just combo logic we could only look at the current value of X, but now we can take 4 separate actions when X=0)
© Mark Redekopp, All rights reserved State Machine Analysis Review 6 Steps to analyze Excitation Equations • Eqn‟s for FF inputs Transition Equations (Q i * = ??) Use characteristic equation of FF and substitute excitation equations for the FF inputs Output Equations Transition/Output Table Make a table showing all combinations of current state and external inputs and then what each of the next state and output values will be for each of those combinations State Name Assignment Symbolic names replace binary codes Draw the State Diagram D-FF: Q* = D RS- FF: Q* = S + R‟Q JK- FF: Q* = JQ‟ + K‟Q

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© Mark Redekopp, All rights reserved State Machine Design State machine design involves taking a problem description and coming up with a state diagram and then designing a circuit to implement that operation Problem Description State Diagram Circuit Implementation
© Mark Redekopp, All rights reserved State Machine Design Coming up with a state diagram is non- trivial Requires creative solutions Designing the circuit from the state diagram is done according to a simple set of steps

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© Mark Redekopp, All rights reserved Solving Problems w/ State Diagrams To come up w/ a state diagram to solve a problem Write out an algorithm or series of steps to solve the problem Each step in your algorithm will usually be one state in your state diagram Ask yourself what past inputs need to be remembered and that will usually lead to a state representation
© Mark Redekopp, All rights reserved 6 Steps of State Machine Design 1. State Diagram 2. Transition/Output Table 3. State Assignment Determine the # of FF‟s required Assign binary codes to replace symbolic names 4. Choose FF type / Excitation Table 5. K-Maps for NSL and OFL One K-Map for every FF input One K-Map for every output of OFL 6. Draw out the circuit

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© Mark Redekopp, All rights reserved Sensor Broken Tooth Clogged Tooth Tooth Space Fly Wheel Example Determine the functionality (or “health” of a fly wheel Healthy if teeth and spaces alternate Unhealthy if tooth breaks off (i.e. 2 consecutive spaces) or if a space gets clogged (i.e. 2 consecutive teeth) Sensor, S, outputs 1 when it sees a tooth, 0 when it sees a space Healthy Fly Wheel Unhealthy Fly Wheel
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## This note was uploaded on 11/08/2009 for the course EE 101 at USC.

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EE101Lecture20 - Introduction to Digital Logic Lecture 20:...

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