IF YOU COULD INCLUDE ALL STEPS PLEASE INCLUDE ALL STEPS WANT TO LEARN

$($HAND WRITTEN PREFERABLY$)$ IF YOU COULD SLOVE QUUESTION

$2$ FIRST then rest I WILL RATE FAST PLEASE REFER TO PICTURES FOR FUNCTIONS

a$.$ Write the function as a sum of minterms. Put your final answer here but show your work on your

calculations pages.

b$.$ Write the function as a product of maxterms. Put your final answer here.

c$.$ Draw a logic diagram for the original function on your calculations pages.

d$.$ Simplify the function using Boolean algebra. Put your final answer here.

Optimize the following functions using a Karnaugh map. Put final answers below, but show K$-$map

work on calculations pages.

a$.F(x,Y,Z)=\frac{\stackrel{}{x}}{b}ar(Z)+\frac{Y}{b}ar(Z)+xYZ.$ Put your final answer here in SOP form.

b$.F(A,B,C)={\displaystyle \underset{?}{\overset{?}{}}}m(0,1,4,5,6).$ Put your final answer here in SOP form.