EE101Lecture18

EE101Lecture18 - Introduction to Digital Logic Lecture 18:...

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© Mark Redekopp, All rights reserved Introduction to Digital Logic Lecture 18: Latches Flip-Flops
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© Mark Redekopp, All rights reserved Bistables vs. Latches Latches Clock input outputs can only change during a specific time When C=1, outputs respond to inputs When C=0, outputs hold their value Bistables • No clock input – outputs can change anytime the inputs change
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© Mark Redekopp, All rights reserved D-Latch • To show that Q remembers its value we can put it in the past tense: –Q = Q 0 (Current Value of Q = Old Value of Q) • OR put it in the future tense – Q* = Q (Next Value of Q = Current Value of Q) 0 1 1 1 1 0 0 1 Q Q x 0 Q * Q* D C 0 1 1 1 1 0 0 1 Q 0 Q 0 x 0 Q Q D C Indicates “next-value” of Q Current Value = Old Value Next Value = Current Value
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© Mark Redekopp, All rights reserved Adding a Sequence of Numbers • Suppose we have a sequence of numbers that comes in over time that we want to sum up • Possible solution: Route the outputs back to the inputs so we can add the current sum to the input X • Problem 1: No way to initialize sum • Problem 2: Outputs can race around to inputs and be added more than once per input number Possible Solution Outputs feedback to inputs and update them sum more than once per input 9,3,2 A0 A1 A2 A3 B0 B1 B2 B3 S0 S1 S2 S3 ‘283 X0 X1 X2 X3 Z0 Z1 Z2 Z3
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© Mark Redekopp, All rights reserved Adding a Sequence of Numbers Time: 0 Suppose somehow we can initialize outputs to 0 Input X = 2 2+0 = 2 2 0 2 A0 A1 A2 A3 B0 B1 B2 B3 S0 S1 S2 S3 ‘283 X0 X1 X2 X3 Z0 Z1 Z2 Z3
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© Mark Redekopp, All rights reserved Adding a Sequence of Numbers Time: 1 Output of 2 feeds back around to the inputs The X = 2 input hasn’t changed Adder adds 2+2 = 4 It doesn’t wait until X changes to the next number 2 2 4 A0 A1 A2 A3 B0 B1 B2 B3 S0 S1 S2 S3 ‘283 X0 X1 X2 X3 Z0 Z1 Z2 Z3
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© Mark Redekopp, All rights reserved Adding a Sequence of Numbers Time: 2 Output of 4 feeds back around to the inputs again The X = 2 input still hasn’t changed Adder adds 2+4 = 6 2 4 6 Problem: We have an uncontrolled feedback loop Problem: We have an uncontrolled feedback loop A0 A1 A2 A3 B0 B1 B2 B3 S0 S1 S2 S3 ‘283 X0 X1 X2 X3 Z0 Z1 Z2 Z3
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© Mark Redekopp, All rights reserved Adding a Sequence of Numbers • Add logic at outputs to just capture and remember the new sum until we’re ready to input the next number in the sequence This logic should remember (i.e. sequential logic) the sum and only update it when the next number arrives 9, 3, 2 Just remember initial sum of 2 until 3 arrives.
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EE101Lecture18 - Introduction to Digital Logic Lecture 18:...

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