8 차시

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Example) sequence detector

Functional specification: Detects three or more consecutive 1’s in a string of bits coming through an input line

1) state diagram

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synthesis using D flip-flops

2) assign binary codes to the states and obtain resulting state table

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3) Choose two D type flip-flop, label them as A and B, one input x, one output y.

)7,6(),,(

)7,5,1(),,()1(

)7,5,3(),,()1(

xBAy

xBADtB

xBADtA

B

A

input equations

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4) simplify the input and output equations

ABy

xBAxD

BxAxD

B

A

'

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5) Draw the logic diagram

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Excitation table

Design with other than D flip-flop input equations must be derived indirectly from the state table

Need a table that lists the required inputs for a given change of state excitation table

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synthesis using JK flip-flops

Use this to determine the flip-flop input equations

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example (use JK flip-flop)

one input, no output two flip-flops (label A and B)

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use the excitation table for JK flip-flop to determine the flip-flop input derive the truth table for the combinational circuit (input=present state+external inputs, output=flip-flop inputs+external output) derive the flip-flop function from the truth table (apply the map) draw the logic diagram

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synthesis using T flip-flops

counter : a sequential circuit that goes through a prescribed sequence of states upon the input pulse input pulse may be clock pulse or an external input binary counter : counter that follows the binary sequence

-No input, no output -Use T flip-flop

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flip-flop input function?

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Logic diagram?

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Counter with non-binary sequence

BCD counter

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- six states, states 011 & 111 are not used - KB and KC have only 1’s and X’s

All 1’s

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- flip-flop input function?

JA=B KA=B JB=C KB=1 JC=B’ KC=1

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effect of the unused states What happens if in ABC=011?

JA=KA=JB=KB=KC=1, JC=0

So, flip-flop A&B complement, and flip-flop C reset.

Next ABC=100

State diagram?

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