Realizing Boolean functions – is a multiplexer (MUX) effectively an application of sum-of-products (SOP) logic, capable of implementing arbitrary Boolean expressions by appropriate input wiring and select control?

Introduction / Context:
The sum-of-products (SOP) form is a canonical way to express Boolean functions as ORs of ANDed literals. Hardware building blocks such as multiplexers, decoders, and programmable logic devices can all realize SOP expressions. This question asks if a multiplexer is, in practice, an application of SOP logic for implementing arbitrary Boolean functions.

Given Data / Assumptions:

• Multiplexer selects one of several data inputs under control of select lines.
• Data inputs may be wired to constants 0/1 or to product terms.
• Goal is to map minterms of the function to MUX inputs.

Concept / Approach:
A 2^k-to-1 MUX uses k select lines to choose one of 2^k inputs. By assigning each input to represent a minterm (product term) and wiring it to logic 1 for minterms belonging to the function (and 0 otherwise), the MUX output becomes the OR (sum) of selected product terms—an SOP realization. Alternatively, with input variables partitioned between data and select lines, a MUX implements complex expressions compactly, mirroring SOP behavior through selection rather than explicit AND-OR gates.

Step-by-Step Solution:

Verification / Alternative check:
Textbook design methods “realize F with a MUX” explicitly treat it as mapping minterms to constant inputs—a direct SOP implementation via selection.

Why Other Options Are Wrong:
Decoders, PLAs, and PALs also realize SOP, but multiplexers certainly can; limiting the capability to 2-to-1 devices or excluding MUX is incorrect.

Common Pitfalls:
Forgetting to account for don’t-care terms; misassigning select/data roles leading to excess hardware.

Final Answer:
Correct