Multiplexer tree; 16:1 MUX from 4:1

Multiplexer tree

A multiplexer tree is the connection of small multiplexers in levels to make a larger multiplexer. The first level selects within groups using the lower select bits, and the next level selects one group using the higher select bits.

16:1 MUX from 4:1 MUXes

A 16:1 MUX has inputs $I_0$–$I_{15}$ and four select lines $S_3S_2S_1S_0$. Use five 4:1 MUXes:

• Level 1: four 4:1 MUXes (M1–M4) with selects $S_1S_0$. M1 gets $I_0$–$I_3$, M2 gets $I_4$–$I_7$, M3 gets $I_8$–$I_{11}$, M4 gets $I_{12}$–$I_{15}$.
• Level 2: one 4:1 MUX (M5) with selects $S_3S_2$ picks one of the outputs of M1–M4.

             S1 S0
 I0-I3   -->[ M1 ]--Y1--+
 I4-I7   -->[ M2 ]--Y2--+--> I0..I3 of
 I8-I11  -->[ M3 ]--Y3--+    [ M5 ] ----> Y
 I12-I15 -->[ M4 ]--Y4--+     S3 S2

Example: $S_3S_2S_1S_0 = 1011$. Every level-1 MUX selects its input 3, so M3 outputs $I_{11}$. M5 with $S_3S_2 = 10$ selects M3, so $Y = I_{11}$, which is input number $1011_2 = 11$. Correct.