Final answer:
A 16:1 multiplexer requires 4 select inputs to choose from among its 16 channels, following the formula 2^S = number of lines, where S equals the number of select inputs needed.
Step-by-step explanation:
To determine how many select inputs are required for a 16:1 multiplexer (mux), we need to know how many different states, or channels, the mux can select from. A 16:1 mux means it can select one of 16 different input lines. The number of select inputs (S) can be calculated using the formula 2^S = number of lines, where S must be an integer.
In this case, for a 16:1 mux:
2^S = 16
S = log2(16)
S = 4
Therefore, 4 select inputs are required to control a 16:1 mux.