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EE101Lecture10

EE101Lecture10 - Introduction to Digital Logic Lecture 10...

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© Mark Redekopp, All rights reserved Introduction to Digital Logic Lecture 10: Karnaugh Maps Decoders
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© Mark Redekopp, All rights reserved Designing Circuits w/ K-Maps Given a description… Block Diagram Truth Table K-Map for each output bit (each output bit is a separate function of the inputs) 3-bit unsigned incrementer If X[2:0] = 000 then Z[2:0] = 001, etc. 3-bit Unsigned Incrementer 3 X[2:0] Z[2:0] 3
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© Mark Redekopp, All rights reserved 3-bit Number Incrementer X 2 X 1 X 0 Z 2 Z 1 Z 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 0 1 0 0 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 0 0 0 0 0 1 1 0 1 0 1 X 2 X 1 X 0 00 01 11 10 0 1 0 1 2 3 6 7 4 5 Z 2 = X 2 X 0 ’ + X 2 X 1 ’ + X 2 ’X 1 X 0 1 1 1 1 0 0 0 0 00 01 11 10 0 1 0 1 2 3 6 7 4 5 Z 0 = X 0 0 1 1 0 1 0 0 1 00 01 11 10 0 1 0 1 2 3 6 7 4 5 Z 1 = X 1 X 0 ’ + X 1 ’X 0 X 2 X 1 X 0 X 2 X 1 X 0
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© Mark Redekopp, All rights reserved Decoders A decoder is a building block that: Takes in an n-bit binary number as input Decodes that binary number and activates the corresponding output Individual outputs for EVERY input combination (i.e. 2 n outputs) D0 D1 D2 D3 D4 D5 D6 D7 X (MSB) Y Z (LSB) 1 output for each combination of the input number 3-bit binary number
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© Mark Redekopp, All rights reserved Decoders A decoder is a building block that: Takes a binary number as input Decodes that binary number and activates the corresponding output Put in 6=110, Output 6 activates (‘1’) Put in 5=101, Output 5 activates (‘1’) D0 D1
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