Question

A Dz. B a E B D A Circuit 1 Circuit 2 Based on the image, select all true statements. Tip: draw truth tables! Circuit 1 is eq
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Answer #1

Solution

Circuit 1

A B C A.B B+C B.C (B+C).(B.C) (A.B)+((B+C).(B.C))
0 0 0 0 0 0 0 0
0 0 1 0 1 0 0 0
0 1 0 0 1 0 0 0
0 1 1 0 1 1 1 1
1 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0
1 1 0 1 1 0 0 1
1 1 1 1 1 1 1 1

Circuit 2

C B A B.C B+C (B.C).(B+C) B.A ((B.C).(B+C)) + B.A
0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 0 0 1 0 0 0
0 1 1 0 1 0 1 1
1 0 0 0 1 0 0 0
1 0 1 0 1 0 0 0
1 1 0 1 1 1 0 1
1 1 1 1 1 1 1 1

From the above truth tables we can see that the circuits are equivalent.

Circuit 1 is eqivalent to the boolean expression Q=(A and B) or ((B or C) and( C and B))

Circuit 2 is eqivalent to the boolean expression Q = (( B and C) and (B or C) ) or (B and A)

So option 1, 3 and 4 are correct.

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