Multiplexer Fundamentals — Select Lines vs. Inputs How many data select lines are required by a multiplexer to select exactly eight distinct inputs (one-hot to binary selection)?

Introduction / Context:
A multiplexer (MUX) routes one of several input lines to a single output based on the value of binary select lines. Understanding the relationship between the number of inputs and the number of select lines is fundamental in data routing and bus design.

Given Data / Assumptions:

• Number of inputs to be selected: 8.
• Select lines are binary encoded signals.
• Only one input is forwarded at a time.

Concept / Approach:
The number of select lines n must satisfy 2^n ≥ number_of_inputs. For exactly 8 inputs, find n such that 2^n = 8. Solving gives n = 3.

Step-by-Step Solution:
Compute powers of two: 2^1 = 2, 2^2 = 4, 2^3 = 8.Match to inputs: 8 inputs correspond to 2^3.Therefore, n = 3 select lines are needed.These lines encode values 000 through 111 to choose inputs 0 through 7.

Verification / Alternative check:
Check a standard 8-to-1 MUX datasheet: devices labeled “8:1 MUX” universally specify 3 select inputs S2, S1, S0.

Why Other Options Are Wrong:

• 1 and 2: Only provide 2 or 4 choices.
• 4: Would select up to 16 inputs, which exceeds the requirement.

Common Pitfalls:
Confusing decoder select lines with enable lines, or forgetting that select lines are binary encoded, not one line per input.

Final Answer:
3