8-to-1 multiplexer design capacity: What is the largest truth table size (number of rows) that can be implemented directly using a single 8-line-to-1-line MUX with 3 select inputs?

Introduction / Context:Multiplexers (MUXes) can implement combinational functions by steering one of many data inputs to the output based on select lines. The number of select lines determines how many input combinations are directly addressable, which in turn determines the size of the truth table that can be realized without extra logic.

Given Data / Assumptions:

• An 8-to-1 MUX has 8 data inputs and 3 select lines.
• No additional external gating or input encoding is used (direct implementation).
• One output bit is produced.

Concept / Approach:With 3 select lines, there are 2^3 = 8 possible select codes. Each select code chooses one of the 8 data inputs, which can be tied to constant 0/1 or other signals to implement the required function. Therefore, the directly realizable truth table has 8 distinct input cases along the select dimensions.

Step-by-Step Solution:

Verification / Alternative check:General rule: an M-to-1 MUX where M = 2^k implements any 1-bit function of k variables directly. Here k = 3, so any function of three variables fits in 8 rows.

Why Other Options Are Wrong:

Common Pitfalls:Confusing data inputs with select inputs; assuming a MUX directly implements functions of more variables than it has select lines; forgetting that constants can be tied to unused data inputs.

Final Answer:8 rows