The Boolean expression Y = A BC + A C can be realised with which of the following gate configurations. Choose the correct answer from the options given below:
- B, C Only
- A, B, C Only
- A, B Only
- A, C Only
Answer
(3) A, B Only
Solution
A: Three NOT gates give A, B, C; the 3-input AND gives A BC; the 2-input AND gives A C; the 2-input OR adds them Y. A is possible.
B: By De Morgan's theorem, A C = A + C = output of a 2-input NOR gate with inputs A and C.
One NOT gate gives B 3-input AND gives A BC; the 2-input OR adds the two terms Y. B is possible.
C: With a 3-input OR, A BC = A + B + C needs NOT gates on A, C and on the OR output (all 3 NOT gates). The AND gate then gives A C, but no OR gate is left to add the two terms C is not possible.
A and B only.
Answer: (3)