1. Implement a 16:1 multiplexer by 4:1 multiplexers, and implement

I₀

I₄

I₈

I₁₂

Implementation of 16:1 Mux:

I₁

I₅

I₉

I₁₃

F

I₃

I₇

I₁₁

I₁₅

I₂

I₆

I₁₀

I₁₄

I₀ …I₁₅ are minterms. To implement F, just set the corresponding input

I [0,1,3,5,8,12,14,15] = 1, others are zeros.

2. Based on the above, if you have another 1:16 decoder, but you cannot directly input 1 or 0 to the multiplexers, what to do?

Let I [0,1,3,5,8,12,14,15] = Out [0,1,3,5,8,12,14,15] (in-order connection)

Let other inputs of Mux have out of order connection with the outputs of DEC. For example, I₂ can be connected with any Out_i except Out₂.