Short note: MUX tree

A MUX tree is a way of building a large multiplexer from several smaller multiplexers connected in levels (a tree). It is used when a single IC with enough inputs is not available.

• The first level of small MUXes receives the data inputs. The lower-order select lines are applied to all of them in common.
• The outputs of the first level go to the data inputs of the next level, which is driven by the higher-order select lines.
• The last MUX gives the final output $Y$.

Example: 8:1 MUX from 2:1 MUXes (needs 4 + 2 + 1 = 7 MUXes):

I0,I1 -[2:1]-+
I2,I3 -[2:1]-+-[2:1]-+
I4,I5 -[2:1]-+       +-[2:1]--> Y
I6,I7 -[2:1]-+-[2:1]-+
      ^S0       ^S1     ^S2

Similarly a 16:1 MUX can be built from five 4:1 MUXes (four in the first level using $S_1S_0$, one in the second level using $S_3S_2$).

Advantages: large MUX from standard small ICs; easy to expand. Drawback: more ICs and more propagation delay (one MUX delay per level).