Discussion
How many select lines does an 8-to-1 multiplexer require?
Answer: C
Correct answer: 3
A multiplexer with \( n \) select lines can choose among \( 2^{n} \) inputs, so for eight inputs \[ 2^{n} = 8 \quad\Rightarrow\quad n = 3. \] The three select lines form a binary address: 000 routes input 0 to the output, 001 routes input 1, and so on up to 111 for input 7. The same relation gives 2 select lines for a 4-to-1 multiplexer and 4 for a 16-to-1. It is the identical arithmetic that determines the number of flip-flops in a counter and the number of address lines for a memory, so it is worth being fluent in both directions. Multiplexers are used for far more than data routing. Because a \( 2^{n} \)-to-1 multiplexer can implement any Boolean function of \( n \) variables directly - by wiring the truth table values to its data inputs - it serves as a general-purpose logic element, which is why lookup tables in field-programmable gate arrays are built this way.
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