Functional replacement by a multiplexer (MUX) In digital design, a single multiplexer can effectively take the place of which of the following elements when used to implement an arbitrary truth table or selection logic?

Introduction / Context:Multiplexers (MUXes) are universal combinational building blocks. By wiring data inputs to logic 0/1 (or signals) and steering with select lines, a MUX can implement many logic functions that would otherwise require multiple small-scale integration (SSI) gates. Understanding this equivalence helps minimize chip count and PCB area.

Given Data / Assumptions:

• A standard n-to-1 multiplexer is available (e.g., 4:1, 8:1, 16:1).
• We can tie MUX inputs to constants or real signals.
• Select lines represent address bits of a truth table.

Concept / Approach:Any truth table with up to n selectable minterms can be realized by mapping select lines to the table’s variables and data inputs to the desired output values for each address. This directly replaces networks of AND/OR/NOT gates used in sum-of-products or other combinational forms.

Step-by-Step Solution:

Verification / Alternative check:Compare gate counts: implementing a 4-variable logic function via canonical SOP may require numerous gates, whereas a single 16:1 MUX plus inverters on select lines can implement the same function compactly and predictably.

Why Other Options Are Wrong:

• “Several Ex-NOR gates”: overly specific; a MUX can emulate them but also far more.
• Only “SSI gates” or only “combinational circuits” is incomplete. The best description includes both.
• Counters are sequential devices; a MUX cannot replace their state storage.

Common Pitfalls:

• Ignoring the need for input inversion; sometimes inverters on select lines are required.
• Overlooking propagation delay and fan-out when replacing large gate networks.

Final Answer:several SSI logic gates or combinational logic circuits