How do you design an 8-to-1 multiplexer using a 2-to-1 multiplexer?

To design an 8-to-1 multiplexer using 2-to-1 multiplexers, you can cascade multiple 2-to-1 MUXes. First, use seven 2-to-1 MUXes to select between the eight input lines (let's call them I0 to I7). The first layer consists of four MUXes combining pairs of inputs, producing four outputs. In the second layer, two additional MUXes combine these four outputs into two, and finally, one last 2-to-1 MUX selects between the last two outputs, giving you a single output based on the 3-bit select lines.