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 equivalent to Circuit 2. Circuit 1 is equivalent to the boolean expression: "Q = (A and B) and ((B or C) and (C and B)" Circuit 2 is equivalent to the boolean expression: "Q = ((B and C) and (B or C)) or (B and A)" Circuit 1 is equivalent to the boolean expression: "Q = (A and B) or ((B or C) and (C and B))" Circuit 2 is equivalent to the boolean expression: "Q = (C and B) or ((B or C) and (A and B))" Circuit 1 is not equivalent to Circuit 2.

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.