1. Quine-McCluskey Algorithm Gautam Singh

2. Outline: step 1 Find Prime Implicants: 1)Find all the minterms and sort by number of 1 bits (these are implicants) 2)Compare every implicant with n 1-bits to all implicants with n+1 1-bits. 3)Combine implicants that vary by a single bit. Replace the bit with an X. 4)Check off implicants that have been 'used' 5)Cross off duplicate implicants. 6)Repeat steps 2 through 5 until no more minterms can be combined 7)The prime implicants are those that were not checked off.

3. Outline: step 2 Find Essential Prime Implicants: Make a prime implicant chart with minterms as columns and prime implicants as rows Look for columns that are 'covered' by only a single prime implicant. These are called “Essential Prime Implicants.” Put a check next to them and also check off all the columns they cover. Among the remaining columns, select the fewest amount of remaining prime implicants that cover them.

4. ABCY 0000 0011 0101 0111 10 00 1011 1101 1111 111 111

5. ABCY 0000 0011 0101 0111 1000 1011 1101 1111 #1 bitsimplicants 1001 1010 2011 2101 2110 3111 111 111

6. ABCY 0000 0011 0101 0111 1000 1011 1101 1111 #1 bitsimplicants 1001 1010 2011 2101 2110 3111 implicants 0X1 X01 01X X10 X11 1X1 11X 111 111

7. ABCY 0000 0011 0101 0111 1000 1011 1101 1111 #1 bitsimplicants 1001 1010 2011 2101 2110 3111 implicants 0X1 X01 01X X10 X11 1X1 11X implicants XX1 X1X 111 111

8. ABCY 0000 0011 0101 0111 1000 1011 1101 1111 #1 bitsimplicants 1001 1010 2011 2101 2110 3111 implicants 0X1 X01 01X X10 X11 1X1 11X implicants XX1 X1X 111 111 XX1 X1X

9. ABCY 0000 0011 0101 0111 1000 1011 1101 1111 001010011101110111 XX1 X1X 111 111

10. ABCY 0000 0011 0101 0111 1000 1011 1101 1111 001010011101110111 XX1 X1X 111 111

11. ABCDY 00000 00010 00101 00111 01000 01010 01101 01111 1000X 1001X 10100 10110 1100X 1101X 11101 1111X

12. ABCDY 00000 00010 00101 00111 01000 01010 01101 01111 1000X 1001X 10100 10110 1100X 1101X 11101 1111X 1 bitsimplicants 10010 11000 20011 20110 21001 21100 30111 31101 31110 41111

13. ABCDY 00000 00010 00101 00111 01000 01010 01101 01111 1000X 1001X 10100 10110 1100X 1101X 11101 1111X 1 bitsimplicants 10010 11000 20011 20110 21001 21100 30111 31101 31110 41111 001X 0X10 100X 1X00 0X11 011X X110 1X01 110X 11X0 X111 11X1 111X

14. ABCDY 00000 00010 00101 00111 01000 01010 01101 01111 1000X 1001X 10100 10110 1100X 1101X 11101 1111X 1 bitsimplicants 10010 11000 20011 20110 21001 21100 30111 31101 31110 41111 001X 0X10 100X 1X00 0X11 011X X110 1X01 110X 11X0 X111 11X1 111X 0X1X 1X0X X11X 11XX

15. ABCDY 00000 00010 00101 00111 01000 01010 01101 01111 1000X 1001X 10100 10110 1100X 1101X 11101 1111X 1 bitsimplicants 10010 11000 20011 20110 21001 21100 30111 31101 31110 41111 001X 0X10 100X 1X00 0X11 011X X110 1X01 110X 11X0 X111 11X1 111X 0X1X 1X0X X11X 11XX 0X1X 1X0X X11X 11XX

16. ABCDY 00000 00010 00101 00111 01000 01010 01101 01111 1000X 1001X 10100 10110 1100X 1101X 11101 1111X 00100011011001111110 11XX X11X 1X0X 0X1X

17. ABCDY 00000 00010 00101 00111 01000 01010 01101 01111 1000X 1001X 10100 10110 1100X 1101X 11101 1111X 00100011011001111110 11XX X11X 1X0X 0X1X

18. ABCDY 00000 00010 00101 00111 01000 01010 01101 01111 1000X 1001X 10100 10110 1100X 1101X 11101 1111X 00100011011001111110 11XX X11X 1X0X 0X1X 11 11 XXX1 XX

19. ABCDEY 000001 000011 000100 000110 001001 001011 001100 001110 010000 010010 010100 010110 011000 011010 011101 011111 100001 100011 100100 100110 101001 101011 101100 101110 110000 110010 110100 110111 111000 111010 111100 111111

20. ABCDEY 000001 000011 000100 000110 001001 001011 001100 001110 010000 010010 010100 010110 011000 011010 011101 011111 100001 100011 100100 100110 101001 101011 101100 101110 110000 110010 110100 110111 111000 111010 111100 111111 00000 00001 00100 10000 00101 10001 10100 01110 10101 01111 11011 11111

21. 00000 00001 00100 10000 00101 10001 10100 01110 10101 01111 11011 11111 ABCDEY 000001 000011 000100 000110 001001 001011 001100 001110 010000 010010 010100 010110 011000 011010 011101 011111 100001 100011 100100 100110 101001 101011 101100 101110 110000 110010 110100 110111 111000 111010 111100 111111 0000X 00X00 X0000 00X01 X0001 0010X X0100 1000X 10X00 X0101 10X01 1010X 0111X X1111 11X11

22. 00000 00001 00100 10000 00101 10001 10100 01110 10101 01111 11011 11111 ABCDEY 000001 000011 000100 000110 001001 001011 001100 001110 010000 010010 010100 010110 011000 011010 011101 011111 100001 100011 100100 100110 101001 101011 101100 101110 110000 110010 110100 110111 111000 111010 111100 111111 0000X 00X00 X0000 00X01 X0001 0010X X0100 1000X 10X00 X0101 10X01 1010X 0111X X1111 11X11 00X0X X000X 00X0X X0X00 X000X X0X00 X0X01 X010X 10X0X

23. 00000 00001 00100 10000 00101 10001 10100 01110 10101 01111 11011 11111 ABCDEY 000001 000011 000100 000110 001001 001011 001100 001110 010000 010010 010100 010110 011000 011010 011101 011111 100001 100011 100100 100110 101001 101011 101100 101110 110000 110010 110100 110111 111000 111010 111100 111111 0000X 00X00 X0000 00X01 X0001 0010X X0100 1000X 10X00 X0101 10X01 1010X 0111X X1111 11X11 00X0X X000X 00X0X X0X00 X000X X0X00 X0X01 X010X 10X0X 00X0X X000X X0X00 X0X01 X010X 10X0X

24. 00000 00001 00100 10000 00101 10001 10100 01110 10101 01111 11011 11111 ABCDEY 000001 000011 000100 000110 001001 001011 001100 001110 010000 010010 010100 010110 011000 011010 011101 011111 100001 100011 100100 100110 101001 101011 101100 101110 110000 110010 110100 110111 111000 111010 111100 111111 0000X 00X00 X0000 00X01 X0001 0010X X0100 1000X 10X00 X0101 10X01 1010X 0111X X1111 11X11 00X0X X000X 00X0X X0X00 X000X X0X00 X0X01 X010X 10X0X 00X0X X000X X0X00 X0X01 X010X 10X0X X0X0X

25. 000000000100100001010111001111100001000110100101011101111111 X0X0X 11X11 X1111 0111X

26. 000000000100100001010111001111100001000110100101011101111111 X0X0X 11X11 X1111 0111X

27. 000000000100100001010111001111100001000110100101011101111111 X0X0X 11X11 X1111 0111X

28. ABCDY 0000 1 0001 1 0010 0 0011 0 0100 1 0101 1 0110 X 0111 1 1000 0 1001 0 1010 1 1011 0 1100 0 1101 1 1110 1 1111 1

29. ABCDY 0000 1 0001 1 0010 0 0011 0 0100 1 0101 1 0110 X 0111 1 1000 0 1001 0 1010 1 1011 0 1100 0 1101 1 1110 1 1111 1