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Truth table, Karnaugh map & logic circuit with 5 outputs and 8 inputs

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Abir Chowdhury
Abir Chowdhury

This is the Logic circuit which enables taking the MW data from the consumers to the substation, separating them into two major categories: a fixed cost for any 4 loads, and cost will increment from 5th load onwards.

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Truth table with 5 outputs and 8 inputs: A B C D E F G H F1 F2 F3 F4 F5 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0
0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0
1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1 0 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0
1 1 0 0 1 1 1 0 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 1 0 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 1 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 1 0 1 0 0 0 0 1 1 1 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0
Karnaugh Map for the 5 output variables: For F5: 0000 0001 0011 0010 0100 0101 0111 0110 1000 1001 1011 1010 1100 1101 1111 1110 E’F’G’H’ E’F’G’H E’F’GH’ E’FG’H’ EF’G’H’ E’F’GH E’FG’H E’FGH’ EF’G’H EF’GH’ EFG’H’ E’FGH EF’GH EFG’H EFGH’ EFGH 0000 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A’B’C’D’ 0001 A’B’C’D 0011 A’B’CD 0010 A’B’CD’ 0100 A’BC’D’ 0101 A’BC’D 0111 A’BCD 0110 A’BCD’ 1000 AB’C’D’ 1001 AB’C’D 1011 AB’CD 1010 AB’CD’ 1100 ABC’D’ 1101 ABC’D 1111 ABCD 1110 ABCD’ F5= A’B’C’D’
For F4: 0000 0001 0011 0010 0100 0101 0111 0110 1000 1001 1011 1010 1100 1101 1111 1110 E’F’G’H’ E’F’G’H E’F’GH’ E’FG’H’ EF’G’H’ E’F’GH E’FG’H E’FGH’ EF’G’H EF’GH’ EFG’H’ E’FGH EF’GH EFG’H EFGH’ EFGH 0000 A’B’C’D’ 0001 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A’B’C’D 0011 A’B’CD 0010 A’B’CD’ 0100 A’BC’D’ 0101 A’BC’D 0111 A’BCD 0110 A’BCD’ 1000 AB’C’D’ 1001 AB’C’D 1011 AB’CD 1010 AB’CD’ 1100 ABC’D’ 1101 ABC’D 1111 ABCD 1110 ABCD’ F4= A’B’C’D
For F3: 0000 0001 0011 0010 0100 0101 0111 0110 1000 1001 1011 1010 1100 1101 1111 1110 E’F’G’H’ E’F’G’H E’F’GH’ E’FG’H’ EF’G’H’ E’F’GH E’FG’H E’FGH’ EF’G’H EF’GH’ EFG’H’ E’FGH EF’GH EFG’H EFGH’ EFGH 0000 A’B’C’D’ 0001 A’B’C’D 0011 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A’B’CD 0010 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A’B’CD’ 0100 A’BC’D’ 0101 A’BC’D 0111 A’BCD 0110 A’BCD’ 1000 AB’C’D’ 1001 AB’C’D 1011 AB’CD 1010 AB’CD’ 1100 ABC’D’ 1101 ABC’D 1111 ABCD 1110 ABCD’ F3= A’B’C
For F2: 0000 0001 0011 0010 0100 0101 0111 0110 1000 1001 1011 1010 1100 1101 1111 1110 E’F’G’H’ E’F’G’H E’F’GH’ E’FG’H’ EF’G’H’ E’F’GH E’FG’H E’FGH’ EF’G’H EF’GH’ EFG’H’ E’FGH EF’GH EFG’H EFGH’ EFGH 0000 A’B’C’D’ 0001 A’B’C’D 0011 A’B’CD 0010 A’B’CD’ 0100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A’BC’D’ 0101 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A’BC’D 0111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A’BCD 0110 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A’BCD’ 1000 AB’C’D’ 1001 AB’C’D 1011 AB’CD 1010 AB’CD’ 1100 ABC’D’ 1101 ABC’D 1111 ABCD 1110 ABCD’ F2= A’B
For F1: 0000 0001 0011 0010 0100 0101 0111 0110 1000 1001 1011 1010 1100 1101 1111 1110 E’F’G’H’ E’F’G’H E’F’GH’ E’FG’H’ EF’G’H’ E’F’GH E’FG’H E’FGH’ EF’G’H EF’GH’ EFG’H’ E’FGH EF’GH EFG’H EFGH’ EFGH 0000 A’B’C’D’ 0001 A’B’C’D 0011 A’B’CD 0010 A’B’CD’ 0100 A’BC’D’ 0101 A’BC’D 0111 A’BCD 0110 A’BCD’ 1000 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 AB’C’D’ 1001 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 AB’C’D 1011 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 AB’CD 1010 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 AB’CD’ 1100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ABC’D’ 1101 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ABC’D 1111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ABCD 1110 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ABCD’ F1= A
Combinational logic circuit: A F2 B F1 F3 C F4 D F5

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Truth table, Karnaugh map & logic circuit with 5 outputs and 8 inputs

  • 1. Truth table with 5 outputs and 8 inputs: A B C D E F G H F1 F2 F3 F4 F5 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0
  • 2. 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0
  • 3. 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1 0 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0
  • 4. 1 1 0 0 1 1 1 0 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 1 0 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 1 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 1 0 1 0 0 0 0 1 1 1 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0
  • 5. Karnaugh Map for the 5 output variables: For F5: 0000 0001 0011 0010 0100 0101 0111 0110 1000 1001 1011 1010 1100 1101 1111 1110 E’F’G’H’ E’F’G’H E’F’GH’ E’FG’H’ EF’G’H’ E’F’GH E’FG’H E’FGH’ EF’G’H EF’GH’ EFG’H’ E’FGH EF’GH EFG’H EFGH’ EFGH 0000 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A’B’C’D’ 0001 A’B’C’D 0011 A’B’CD 0010 A’B’CD’ 0100 A’BC’D’ 0101 A’BC’D 0111 A’BCD 0110 A’BCD’ 1000 AB’C’D’ 1001 AB’C’D 1011 AB’CD 1010 AB’CD’ 1100 ABC’D’ 1101 ABC’D 1111 ABCD 1110 ABCD’ F5= A’B’C’D’
  • 6. For F4: 0000 0001 0011 0010 0100 0101 0111 0110 1000 1001 1011 1010 1100 1101 1111 1110 E’F’G’H’ E’F’G’H E’F’GH’ E’FG’H’ EF’G’H’ E’F’GH E’FG’H E’FGH’ EF’G’H EF’GH’ EFG’H’ E’FGH EF’GH EFG’H EFGH’ EFGH 0000 A’B’C’D’ 0001 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A’B’C’D 0011 A’B’CD 0010 A’B’CD’ 0100 A’BC’D’ 0101 A’BC’D 0111 A’BCD 0110 A’BCD’ 1000 AB’C’D’ 1001 AB’C’D 1011 AB’CD 1010 AB’CD’ 1100 ABC’D’ 1101 ABC’D 1111 ABCD 1110 ABCD’ F4= A’B’C’D
  • 7. For F3: 0000 0001 0011 0010 0100 0101 0111 0110 1000 1001 1011 1010 1100 1101 1111 1110 E’F’G’H’ E’F’G’H E’F’GH’ E’FG’H’ EF’G’H’ E’F’GH E’FG’H E’FGH’ EF’G’H EF’GH’ EFG’H’ E’FGH EF’GH EFG’H EFGH’ EFGH 0000 A’B’C’D’ 0001 A’B’C’D 0011 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A’B’CD 0010 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A’B’CD’ 0100 A’BC’D’ 0101 A’BC’D 0111 A’BCD 0110 A’BCD’ 1000 AB’C’D’ 1001 AB’C’D 1011 AB’CD 1010 AB’CD’ 1100 ABC’D’ 1101 ABC’D 1111 ABCD 1110 ABCD’ F3= A’B’C
  • 8. For F2: 0000 0001 0011 0010 0100 0101 0111 0110 1000 1001 1011 1010 1100 1101 1111 1110 E’F’G’H’ E’F’G’H E’F’GH’ E’FG’H’ EF’G’H’ E’F’GH E’FG’H E’FGH’ EF’G’H EF’GH’ EFG’H’ E’FGH EF’GH EFG’H EFGH’ EFGH 0000 A’B’C’D’ 0001 A’B’C’D 0011 A’B’CD 0010 A’B’CD’ 0100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A’BC’D’ 0101 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A’BC’D 0111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A’BCD 0110 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A’BCD’ 1000 AB’C’D’ 1001 AB’C’D 1011 AB’CD 1010 AB’CD’ 1100 ABC’D’ 1101 ABC’D 1111 ABCD 1110 ABCD’ F2= A’B
  • 9. For F1: 0000 0001 0011 0010 0100 0101 0111 0110 1000 1001 1011 1010 1100 1101 1111 1110 E’F’G’H’ E’F’G’H E’F’GH’ E’FG’H’ EF’G’H’ E’F’GH E’FG’H E’FGH’ EF’G’H EF’GH’ EFG’H’ E’FGH EF’GH EFG’H EFGH’ EFGH 0000 A’B’C’D’ 0001 A’B’C’D 0011 A’B’CD 0010 A’B’CD’ 0100 A’BC’D’ 0101 A’BC’D 0111 A’BCD 0110 A’BCD’ 1000 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 AB’C’D’ 1001 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 AB’C’D 1011 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 AB’CD 1010 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 AB’CD’ 1100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ABC’D’ 1101 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ABC’D 1111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ABCD 1110 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ABCD’ F1= A
  • 10. Combinational logic circuit: A F2 B F1 F3 C F4 D F5