Draw a circuit that corresponds to the following Boolean equation (use only NOR gates):
Z = A' B' + C
Three NOR gates are needed:
(1) inputs A and B,
(2) inputs output of (1) and C, and
(3) as an inverter for the output of (C)
Fill in the truth table for the function Z.
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Write the function above in canonical sum-of-products form.
Z = A'B'C' + A'B'C + A'BC + AB'C + ABC = Sm(0,1,3,5,7)
Show how you can arrive at the original equation from the sum-of-products form using the axioms/theorems of Boolean algebra (show each step of your work):
Z = A'B'C' + A'B'C + A'BC + AB'C + ABC
Z = A'B'C' + A'B'C + A'B'C + A'BC + AB'C + ABC
(idempotency)
Z = A'B'(C' + C) + C(A'B' + A'B + AB' + AB)
(distributivity)
Z = A'B' + C( A'(B' + B) + A (B' + B) )
(distributivity, complementarity, identity)
Z = A'B' + C(A' + A)
(complementarity, identity)
Z = A'B' + C
(complementarity, identity)