EE101Lecture4

EE101Lecture4 - Lecture 4 Slides Boolean Algebra Logic...

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© Mark Redekopp, All rights reserved Lecture 4 Slides Boolean Algebra Logic Functions Canonical Sums/Products
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© Mark Redekopp, All rights reserved Gates Gates can have more than 2 inputs but the functions stay the same AND = output = 1 if ALL inputs are 1 Outputs 1 for only 1 input combination OR = output = 1 if ANY input is 1 Outputs 0 for only 1 input combination X Y Z F 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 X Y Z F 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 3-input AND 3-input OR F x y z F x y z
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© Mark Redekopp, All rights reserved Checkers / Decoders An AND gate only outputs „1‟ for 1 combination That combination can be changed by adding inverters to the inputs We can think of the AND gate as “checking” or “decoding” a specific combination and outputting a „1‟ when it matches. X Y Z F 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 F x y z X Y Z F 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 F x y z AND gate decoding (checking for) combination 101 AND gate decoding (checking for) combination 000
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© Mark Redekopp, All rights reserved Checkers / Decoders An OR gate only outputs „0‟ for 1 combination That combination can be changed by adding inverters to the inputs We can think of the OR gate as “checking” or “decoding” a specific combination and outputting a „0‟ when it matches. OR gate decoding (checking for) combination 010 X Y Z F 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 F x y z OR gate decoding (checking for) combination 110 X Y Z F 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 1 F x y z
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© Mark Redekopp, All rights reserved Using Decoders to Implement Functions Given an any logic function, it can be implemented with the superposition of decoders/checkers X Y Z F 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1
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© Mark Redekopp, All rights reserved Using Decoders to Implement Functions Given an any logic function, it can be implemented with the superposition of decoders X Y Z F 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 X Y Z A 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 x y z A
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© Mark Redekopp, All rights reserved Using Decoders to Implement Functions Given an any logic function, it can be implemented with the superposition of decoders X Y Z F 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 X Y Z A B 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 x y z z y x A B
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© Mark Redekopp, All rights reserved Using Decoders to Implement Functions Given an any logic function, it can be implemented with the superposition of decoders X Y Z F 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 X Y Z A B C 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 1 1 0 0 1 x y z z y x z y x A B C
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© Mark Redekopp, All rights reserved Using Decoders to Implement Functions Given an any logic function, it can be implemented with the superposition of decoders X Y Z F 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 X Y Z A B C F 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 x y z z y x z y x F A B C
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© Mark Redekopp, All rights reserved Using Decoders to Implement Functions Given an any logic function, it can be implemented with the superposition of decoders X Y Z F 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 X Y Z A B C F 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1
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