Multiplexer tree; 1:16 DEMUX from 1:4

Multiplexer tree

A multiplexer tree is a larger multiplexer built by connecting smaller multiplexers in two or more levels. The lower select bits drive the first-level MUXes and the higher select bits drive the next level, which picks one first-level output. Example: a 16:1 MUX from five 4:1 MUXes. The same idea used with DEMUXes is called a demultiplexer tree.

1:16 DEMUX from 1:4 DEMUXes

A 1:16 DEMUX needs 4 select lines $S_3 S_2 S_1 S_0$. Use five 1:4 DEMUXes in two levels:

• Level 1: one 1:4 DEMUX receives the data input $D$; its selects are the MSBs $S_3 S_2$. It sends $D$ to one of four lines.
• Level 2: four 1:4 DEMUXes, each fed from one level-1 output, all with selects $S_1 S_0$. They give the 16 outputs $Y_0$–$Y_{15}$.

                          S1 S0
                        +-------+
                   +--->|  DM1  |--> Y0  .. Y3
                   |    +-------+
         S3 S2     |    +-------+
       +-------+   | +->|  DM2  |--> Y4  .. Y7
  D -->| DM0  0|---+ |  +-------+
       |      1|-----+  +-------+
       |      2|------->|  DM3  |--> Y8  .. Y11
       |      3|---+    +-------+
       +-------+   |    +-------+
                   +--->|  DM4  |--> Y12 .. Y15
                        +-------+
        (DM1-DM4 all use S1 S0)

Working: if $S_3S_2S_1S_0 = 1001$, DM0 ($S_3S_2 = 10$) sends $D$ to DM3; DM3 ($S_1S_0 = 01$) sends it to its second output, which is $Y_9$. No extra gates are needed.