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

2. 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

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

4. InputsOutput A1A1 A0A0 B1B1 B0B0 A>B 00000 00010 00100 00110 01001 01010 01100 01110 InputsOutput A1A1 A0A0 B1B1 B0B0 A>B 10001 10011 10100 10110 11001 11011 11101 11110 Function Table for A>B svbitec.wordpress.com

5. InputsOutput A1A1 A0A0 B1B1 B0B0 A=B 00001 00010 00100 00110 01000 01011 01100 01110 InputsOutput A1A1 A0A0 B1B1 B0B0 A=B 10000 10010 10101 10110 11000 11010 11100 11111 Function Table for A=B svbitec.wordpress.com

6. InputsOutput A1A1 A0A0 B1B1 B0B0 A<B 00000 00011 00101 00111 01000 01010 01101 01111 InputsOutput A1A1 A0A0 B1B1 B0B0 A<B 10000 10010 10100 10111 11000 11010 11100 11110 Function Table for A<B svbitec.wordpress.com

7. Karnaugh Map for A>B A1A0/B1B0A1A0/B1B0 00011110 000000 011000 111101 101100 svbitec.wordpress.com

8. Karnaugh Map for A=B A1A0/B1B0A1A0/B1B0 00011110 001000 010100 110010 100001 svbitec.wordpress.com

9. Karnaugh Map for A<B A1A0/B1B0A1A0/B1B0 00011110 000111 010011 110000 100010 svbitec.wordpress.com

10. 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

11. Karnaugh Map AB/ CD 00011110 000110 010011 111111 101110 svbitec.wordpress.com

12. Karnaugh Map AB/ CD 00011110 000100 010111 111110 100010 svbitec.wordpress.com

13. 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

14. Quine-McCluskey Method (table1) MintermABCD 10001 30011 60110 70111 81000 91001 111011 121100 131101 141110 151111 svbitec.wordpress.com

15. Quine-McCluskey Method (table2) MintermABCDused 10001 81000 30011 60110 91001 121100 70111 111011 131101 141110 151111 svbitec.wordpress.com

16. Quine-McCluskey Method (table3) ABCDused 1,300-1 1,9-001 8,9100- 8,121-00 3,70-11 3,11-011 6,7011- 6,14-110 9,1110-1 9,131-01 svbitec.wordpress.com

17. Quine-McCluskey Method (table3) ABCDused 12,13110- 12,1411-0 7,15-111 11,151-11 13,1511-1 14,15111- svbitec.wordpress.com

18. Quine-McCluskey Method (table4) ABCDused 1,3,9,11-0-1 8,9,12,131-0- 3,7,11,15--11 6,7,14,15-11- 9,11,13,151--1 12,13,14,1511-- svbitec.wordpress.com

19. Quine-McCluskey Method (table5) 1367891112131415 xxxx xxxx xxxx xxxx xxxx xxxx svbitec.wordpress.com

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

21. Quine-McCluskey Method (table1) MintermABCD 10001 50101 60110 70111 111011 121100 131101 151111 svbitec.wordpress.com

22. Quine-McCluskey Method (table2) MintermABCDUsed 10001 50101 60110 121100 70111 111011 131101 151111 svbitec.wordpress.com

23. 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

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

25. Quine-McCluskey Method (table5) 156711121315 xx xx xx xx xxxx svbitec.wordpress.com

26. 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

27. 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