Final answer:
You need two 2 to 1 multiplexers to synthesize a 4 to 1 multiplexer.
Step-by-step explanation:
In order to synthesize a 4 to 1 multiplexer using 2 to 1 multiplexers, we can use a hierarchical structure. We start by using two 2 to 1 multiplexers and connect their outputs to the inputs of another 2 to 1 multiplexer. This arrangement allows us to select between four different inputs using two select lines.
So, in total, we need two 2 to 1 multiplexers to synthesize a 4 to 1 multiplexer.