Compare the following integrated sub$-$circuits $($multiplexer$,$ decoder, encoder and demultiplexer$)$ with respect to their functionality, inputs, and outputs?

What is a $22$ crossbar switch?

Write a Verilog code to capture the behavior of $22$ crossbar switch.

For the function $f(w_1,w_2,w_3)={\displaystyle \underset{?}{\overset{?}{}}}m(0,2,3,6),$ use Shannon's expansion to derive an implementation using a $2-$to$-1$ multiplexer and any other necessary gates.