The Boolean expression $Y = A\overline BC + \overline A\,\overline C$ can be realised with which of the following gate configurations?
A. One 3-input AND gate, 3 NOT gates, one 2-input OR gate and one 2-input AND gate
B. One 3-input AND gate, 1 NOT gate, one 2-input NOR gate and one 2-input OR gate
C. One 3-input OR gate, 3 NOT gates and one 2-input AND gate
Choose the correct answer from the options given below:
Answer: (B) A, B only
**A**: invert B, A and C with three NOT gates. The 3-input AND gives $A\overline BC$, the 2-input AND gives $\overline A\,\overline C$, and the OR adds them. ✔
**B**: by De Morgan, $\overline A\,\overline C = \overline{A + C}$, which is one 2-input NOR gate. One NOT gives $\overline B$ for the 3-input AND $A\overline BC$, and the OR adds the two terms. ✔
**C**: a single 2-input AND gate cannot form the three-variable product $A\overline BC$, and an OR gate only adds terms together, so these gates cannot build $Y$. ✘
Answer: A and B only.
Solution by Sreeraj P, M.Sc Physics