Question

Assume a function,

Q(A, B, C) = AB + A(B + C) + B(B + C).
Design function Q with logic gates.

Answer 1

To design function Q with logic gates, apply the distributive law to simplify the given function to AB + AC + B, then translate the boolean expression into a circuit using AND and OR gates.

Step-by-step explanation:

The subject of this question is logic gates design, which falls under the Computers and Technology category. The function that needs to be implemented using logic gates is Q(A, B, C) = AB + A(B + C) + B(B + C). To design Q using logic gates, apply the distributive law A(B+C) = AB + AC, which is also applicable in the context of logical operations.

Step 1: Apply distributive law to A(B+C) to get AB + AC.

Step 2: Apply distributive law to B(B+C) to get BB + BC, but since B and B are the same, it simplifies to B + BC.

Step 3: Combine all terms and simplify the equation, if possible, to reduce the number of required logic gates. In this case, AB + A(B + C) + B(B + C) simplifies to AB + AC + B.

Step 4: Translate the simplified boolean expression into logic gates, considering the commutative property A+B = B+A for arranging inputs conveniently and understanding that AB is the AND operation, while A+B is the OR operation.