Digital Logic & Design Vishal Jethava Lecture 12 svbitec.wordpress.com.

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Presentation transcript:

Digital Logic & Design Vishal Jethava Lecture 12 svbitec.wordpress.com

Recap Karnaugh Maps Mapping Standard POS expressions Mapping Non-Standard POS expressions Simplification of K-maps for POS expressions SOP-POS conversion using K-map 5-variable K-map Functions having multiple outputs svbitec.wordpress.com

Comparator Circuit Inputs two 2-bit binary numbers A and B Has three outputs A>B A=B A<B svbitec.wordpress.com

InputsOutput A1A1 A0A0 B1B1 B0B0 A>B InputsOutput A1A1 A0A0 B1B1 B0B0 A>B Function Table for A>B svbitec.wordpress.com

InputsOutput A1A1 A0A0 B1B1 B0B0 A=B InputsOutput A1A1 A0A0 B1B1 B0B0 A=B Function Table for A=B svbitec.wordpress.com

InputsOutput A1A1 A0A0 B1B1 B0B0 A<B InputsOutput A1A1 A0A0 B1B1 B0B0 A<B Function Table for A<B svbitec.wordpress.com

Karnaugh Map for A>B A1A0/B1B0A1A0/B1B svbitec.wordpress.com

Karnaugh Map for A=B A1A0/B1B0A1A0/B1B svbitec.wordpress.com

Karnaugh Map for A<B A1A0/B1B0A1A0/B1B svbitec.wordpress.com

Quine-McCluskey Method Difficult to manage K-maps of more than 4 variables With a 4-varaible K-map optimum groups of 1s and 0s are not formed svbitec.wordpress.com

Karnaugh Map AB/ CD svbitec.wordpress.com

Karnaugh Map AB/ CD svbitec.wordpress.com

Quine-McCluskey Method Programmed based approach Two step method Find Prime Implicants through exhaustive search Selecting minimal set of essential prime implicants svbitec.wordpress.com

Quine-McCluskey Method (table1) MintermABCD svbitec.wordpress.com

Quine-McCluskey Method (table2) MintermABCDused svbitec.wordpress.com

Quine-McCluskey Method (table3) ABCDused 1, , , , , , , , , , svbitec.wordpress.com

Quine-McCluskey Method (table3) ABCDused 12, , , , , , svbitec.wordpress.com

Quine-McCluskey Method (table4) ABCDused 1,3,9, ,9,12, ,7,11, ,7,14, ,11,13, ,13,14, svbitec.wordpress.com

Quine-McCluskey Method (table5) xxxx xxxx xxxx xxxx xxxx xxxx svbitec.wordpress.com

Example 2 Slightly different method that uses binary values svbitec.wordpress.com

Quine-McCluskey Method (table1) MintermABCD svbitec.wordpress.com

Quine-McCluskey Method (table2) MintermABCDUsed svbitec.wordpress.com

Quine-McCluskey Method (table3) MintermsVariable removedused 1,54 5,72 5,138 6,71 12,131 7,158 11,154 13,152 svbitec.wordpress.com

Quine-McCluskey Method (table4) MintermsTerm removedused 5,7,13,152,8 svbitec.wordpress.com

Quine-McCluskey Method (table5) xx xx xx xx xxxx svbitec.wordpress.com

Comparator that compares two 3-bit numbers 6 variables, 64 input combinations Representing the comparator function through function table long and tedious Represent three output functions in terms of minterms Solve by Quine-McClusky method Quine-McCluskey Method svbitec.wordpress.com

Odd Prime Number Circuit Circuit detects odd prime numbers for a 5- bit input number Function represented by minterms 1, 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31 svbitec.wordpress.com