Topic: Digital Electronics
In the following circuit, Y can be expressed as
(The diagram shows a 4-to-1 MUX with inputs $I_0=0, I_1=1, I_2=0, I_3=A$ and select lines $S_1=A, S_0=B$, whose output is connected to the '0' input of a 2-to-1 MUX. The '1' input of the 2-to-1 MUX is connected to B, and its select line is $S=C$. The output is Y.)
- A. $Y=BC+A$
- B. $Y=C$
- C. $Y=AC'+BC$
- D. $Y=B$
Answer: D. $Y=B$
Explanation: For the 4-to-1 MUX, the output is $\overline{A}\overline{B}(0) + \overline{A}B(1) + A\overline{B}(0) + AB(A) = \overline{A}B + AB = B(\overline{A} + A) = B$.
For the 2-to-1 MUX, the inputs are $0 \rightarrow B$ and $1 \rightarrow B$, with select line $C$. The output $Y = \overline{C}B + CB = B(\overline{C} + C) = B$.