EE101Lecture6

EE101Lecture6 - Mark Redekopp, All rights reserved...

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Unformatted text preview: Mark Redekopp, All rights reserved Introduction to Digital Logic Lecture 6: Minterms / Maxterms 2 & 3 Variable Theorems Mark Redekopp, All rights reserved Application: Channel Selector Given 4 input, digital music channels and 4 output channels Given individual select inputs that select 1 input channel to be routed to 1 output channel Channel Selector ICH0 ICH1 ICH2 ICH3 OCH0 OCH1 OCH2 OCH3 ISEL0 ISEL1 ISEL2 ISEL3 OSEL0 OSEL1 OSEL2 OSEL3 4 Input channels 4 Output channels Input Channel Select Output Channel Select 011010101001101 101010110101010 101001010101111 001010101001011 Mark Redekopp, All rights reserved Application: Steering Logic 4-input music channels (ICHx) Select one input channel (use ISELx inputs) Route to one output channel (use OSELx inputs) 011010101001101 101010110101010 101001010101111 001010101001011 ICH0 ICH1 ICH2 ICH3 IS E L0 IS E L1 IS E L2 IS E L3 OSEL0 OSEL1 OSEL2 OSEL3 OCH 0 OCH 1 OCH 2 OCH 3 Mark Redekopp, All rights reserved Application: Steering Logic 1 st Level of AND gates act as barriers only passing 1 channel OR gates combines 3 streams of 0s with the 1 channel that got passed (i.e. ICH1) 2 nd Level of AND gates passes the channel to only the selected output ICH0 ICH1 ICH2 ICH3 I SEL0 I SEL1 I SEL2 I SEL3 OSEL0 O SE L1 OSEL2 OSEL3 OCH 0 OCH 1 OCH 2 OCH 3 0 0 1 1 ICH1 ICH1 1 ICH1 ICH1 ICH1 ICH1 ICH1 1 0 0 OR: 0 + ICH1 + 0 + 0 = ICH1 AND: 1 AND ICH1 = ICH1 0 AND ICH1 = 0 AND: 1 AND ICHx = ICHx 0 AND ICHx = 0 Connection Point Mark Redekopp, All rights reserved Truth Tables to Equations/Circuits Given a circuit with n-inputs, 2 n possible combinations exist => 2 n rows in a T.T. A general approach to converting a T.T. to equation or circuit Build a checker/decoder circuit for each combination and include the combinations where the function should be 1 Mark Redekopp, All rights reserved Finding Equations/Circuits Given a function and checkers (called decoders) for each combination, we just need to OR together the checkers where F = 1 Checker for 000 Checker for 001 Checker for 010 Checker for 011 Checker for 100 Checker for 101 Checker for 110 Checker for 111 3-bit number {x,y,z} X Y Z F 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 F Assume we use AND- gate decoders that output a 1 when the combination is found Mark Redekopp, All rights reserved Boolean Algebra Terminology Literal : A literal is an instance of a single variable or its complement....
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EE101Lecture6 - Mark Redekopp, All rights reserved...

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