CSE370 Quiz 1 (10 April)
 
 

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.
 

A
B
C
Z
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1

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)

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