Input selector bits $($choose $2)=a$

$q,$

$q,$

$q,$

c$\_\_$

d

$q,$

e$\_$

Diagram $=4$:$1$ selector switch $($mux$)$

Data inputs from left, control inputs $($S$)$ from bottom, output to right

For Selector bits $($in alphabetical order$)=00,$ input equation $=$

For Selector $=01$ : $q,$

$$

For Selector $=10$ : $q,$

For Selector $=11$ : $q,$

Example$/$explanation: if you choose a and $b$ as your selector bits, complete the minterms for $!$a$!$b $(00$ case$),!$ab $(01),$ a$!$b $(10),$ and ab $(11),$ using functions of $(c,d,e--$ it's essentially a Shannon decomp. problem. Some choices of selector variables may result in simpler circuits than others.

$5$

$4.$ Logic simplification $,Y=(!B$&$C)|(A$&$!B$&$!C)|(B$&$!C)$

Kmap, if you care to use it:

$\backslash$table$[[,,,,,],[,,,,,],[,,,,,]]$

$\backslash$table$[[,,,,,],[,,,,,],[,,,,,]]$

$4\mathrm{.}1$ Simplify to a minimun sum of products. Show your work. $(12$ points$)$

$4\mathrm{.}2$ Simplify the same to minimum product of sums. Show your work. $(13$ points$)$