For each of the following functions: F = AB\' +BC + AC G = (A+B)(A+C\')+AB\' a)

Question

                    For each of the following functions:                 

                    F = AB' +BC + AC                 

                    G = (A+B)(A+C')+AB'                 

                    a) show the truth table                 

                    b) show an algebraic expression in sum of minterms fom.                 

                    c) show a minimum sum of products expression(F: 2 terms, 4 literals, G:2 terms, 3 literals)                 

                    d) show the minterms of the complement of each function in numeric form.                 

                    e) show an algebraic expression in product of maxterms form.                 

                    f) show minimum POS expression (F: 2 terms, 4 literals; G: 2 terms, 4 literals)                 

Explanation / Answer

G=

b) F= AB'(C+C')+BC(A+A')+AC(B+B')

F=AB'C+AB'C'+ABC+A'BC+ABC+AB'C

F=AB'C+AB'C'+ABC+A'BC

G= (A+B)(A+C')+AB

G=A+AB+BC'+AC'+AB

G=A(1+B+C'+B) +BC'

G=A+BC'

G=A(B+B')(C+C')+BC'(A+A')

G=ABC+AB'C+ABC'+AB'C'+ABC'+A'BC'

G=ABC+AB'C+ABC'+AB'C'+A'BC'

c) F=AB'+BC

G= A+BC'

e) F=sigma(3,4,5,7)

=PI(0,1,2,6) =(A+B+C)(A+B+C')(A+B'+C)(A'+B'C)

G=sigma(2,4,5,6,7)

G=PI(0,1,3) =(A+B+C)(A+B+C')(A+B'+C')

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