Solution Explanation

The question requires matching Boolean functions, given in sum of minterms notation $\sum$, to specific multiplexer (MUX) implementations listed in LIST-II.

Matching Function A

Function A: F(A,B,C,D) = $\sum$ (1,3, 4,11,12,13,14,15). This involves 4 variables (A,B,C,D).

A 4-variable function typically requires an 8x1 MUX (using 3 select lines). Analysis shows that implementing the complement function F' = $\sum$ (0, 2, 5, 6, 7, 8, 9, 10) using an 8x1 MUX requires data inputs that are mostly D' (complemented D). Implementing F' and then inverting the output yields F. Therefore, Function A matches with IV. 8x1 MUX and 1 NOT gate.

Matching Function B

Function B: F(A,B,C) = $\sum$ (1,2,6,7). This involves 3 variables (A,B,C).

A 3-variable function typically uses a 4x1 MUX (using 2 select lines). Analyzing the complement function F' = $\sum$ (0, 3, 4, 5) shows it can be implemented with a 4x1 MUX using select lines A, B, and inputs involving C'. Inverting the output of this F' implementation gives F. Therefore, Function B matches with III. 4x1 MUX and 1 NOT gate.

Matching Function C

Function C: F(A,B,C) = $\sum$ (1,3,5,7). This involves 3 variables.

This function simplifies directly. Using Boolean algebra or a K-map, F(A,B,C) = C. This output can be directly generated using a 4x1 MUX. Therefore, Function C matches with II. 4x1 MUX.

Matching Function D

Function D: F(A,B,C,D) = $\sum$ (1,3,5,7,9,11,13,15). This involves 4 variables.

This sum of minterms represents all odd-numbered minterms. This simplifies directly to F(A,B,C,D) = D. This output can be directly generated using an 8x1 MUX (standard for 4 variables). Therefore, Function D matches with I. 8x1 MUX.

Final Matching

Based on the analysis:

• A matches with IV.
• B matches with III.
• C matches with II.
• D matches with I.

The correct combination is A-IV, B-III, C-II, D-I, which corresponds to Option B.