The input$/$output table for the Boolean function F is

x y z F $($x$,$ y$,$ z$)$

$1110$

$1101$

$1010$

$1001$

$0110$

$0100$

$0011$

$0001$

a$)$ Find the sum$-$of$-$products expansion for F $.$

xy $$z $+$ x $$y $$z $+$x $$yz $+$x $$y $$z

b$)$ Simplify your answer to a$)$ using a Karnaugh map.

yz $$yz $$y $$z y $$z

x $46$

$$x $10$

Boxes $4,6,1$ and $0$ should have $1$s in them.

Boxes $4$ and $6$ merged together represent the term x $$z$.$

Boxes $1$ and $0$ merged together represent the term $$x $$y$.$

x $$z $+$x $$y

c$)$ Simplify your answer to a$)$ using the Quine$-$McCluskey method.

$1.$ xy $$z $11010\{1,2\}$

$2.$ x $$y $$z $10000\{2,4\}$

$3.$x $$yz $00100\{3,4\}$

$4.$x $$y $$z $000$

From lines $1$ and $3,\{1,2\}\backslash$cup $\{3,4\}=\{1,2,3,4\}$ covers all the minterms. x $$z $+$x $$y

d$)$ Draw a circuit that implements this function.