Question

Design a circuit which takes two inputs and outputs a 1 if and only if the two inputs are the same signal. You may only use two 2-Input AND gates, one 2-Input OR gate and two NOT gates.[3]

Answer 1

Answer:

Q = A ⊕ B = (A AND B) + ( not(A) AND not(B) )

Explanation:

AND gates : only output 1 when both inputs are 1

OR gate:  only output 1 when either or both of the inputs are 1

NOT gates: takes only one input ad output the opposite of the input

The required circuit should takes two inputs and outputs a 1 if and only if the two inputs are the same signal.

The two possible scenarios : both input are 1's or 0's

Q = A ⊕ B = (A AND B) + ( not(A) AND not(B) )

A  B  not(A) not(B)  A AND B    not(A) AND not(B)   Q

0  0     1          1            0                      1                       1

0   1      1         0            0                     0                       0

1    0     0        1             0                     0                       0

1     1     0       0              1                     0                       1