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ass2sol - Question 1 a A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 B...

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Question 1 a) A B C D F 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 b) CD 00 01 11 10 AB 00 0 0 0 0 01 1 0 1 1 11 0 0 1 1 10 0 0 1 0 CD 00 01 11 10 AB 00 0 0 0 0 01 1 0 1 1 11 0 0 1 1 10 0 0 1 0 BC+!AB!D+CDA (A+B)(C+!D)(!A+C)(D+B) Algebraic analysis Minterm: !AB!C!D+!ABC!D+!ABCD+ABCD+ABC!D+A!BCD !AB!D(!C+C) + ACD(!B+B) + !ABCD + ABC!D We can add terms without changing the initial expression (overlapping terms) !AB!D+CDA+!ABCD+ABC!D+!ABC!D+ABCD !AB!D+CDA+!ABC(D+!D)+ABC(!D+D) !AB!D+CDA+BC(!A+A) BC+!AB!D+CDA Maxterm: (A+B+C+D)(A+B+C+!D)(A+B+!C+!D)(A+B+!C+D)(A+!B+C+!D)(!A+!B+C+!D)(!A+B+C+!D)(!A+!B+C+D)(!A+B+C +D)(!A+B+C+!D) (ABCD)+(ABC!D)+(AB!C!D)+(AB!CD)+(A!BC!D)+(!A!BC!D)+(!ABC!D)+(!A!BCD)+(!ABCD)+(!ABC!D) (ABC)(D+!D)+(AB!C)(!D+D)+ (A!BC!D)+(!A!BC!D)+(!ABC!D)+(!A!BCD)+(!ABCD)+(!ABC!D)
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(AB)(C+!C)+(A!BC!D)+(!A!BC!D)+(!ABC!D)+(!A!BCD)+(!ABCD)+(!ABC!D)+(ABC!D)+(!A!BC!D)+(!ABC!D)+(!A BCD)+(!AB!CD)+(ABCD)+(AB!CD) (AB)+(C!D!B)(A+A)+(C!DB)(!A+A)+(!ACB)(D+!D)+(!AC!B)(D+!D)+(BD!C)(A+!A)+(BDC)(A+!A) AB+(C!D)(!B+B)+(!AC)(B+!B)+(BD)(!C+C) AB+C!D+!AC+BD Applying the dual (A+B)(C+!D)(!A+C)(B+D) c) (A+B)(C+!D)(!A+C)(D+B)
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