Final answer:
Five 4 to 1 multiplexers are needed to synthesize a 16 to 1 multiplexer; four will be used in the first level to reduce the 16 inputs to 4, and one will be used in the second level to select the final output.
Step-by-step explanation:
To synthesize a 16 to 1 multiplexer using 4 to 1 multiplexers, you need to consider that each 4 to 1 multiplexer can handle 4 input signals. To handle 16 input signals, you would set up a two-level multiplexer structure. In the first level, you would use four 4 to 1 multiplexers, each taking in 4 of the 16 inputs, to narrow down the selection to 4 outputs. These 4 outputs would then be fed into a fifth 4 to 1 multiplexer at the second level to select the final output. Therefore, you need five 4 to 1 multiplexers in total: four for the first level and one for the second level.