Given the truth table below, complete the following questions:

A B C D Out

$00000$

$00010$

$00100$

$00111$

$01000$

$01010$

$01100$

$01110$

$10001$

$10011$

$10100$

$10111$

$11001$

$11011$

$11100$

$11111$

$($The problem continues on the next page.$)$

a$)$ Complete the K$-$map for Out

CD $\backslash$ AB $00011110$

$00$

$01$

$11$

$10$

b$)$ List all prime implicants

c$)$ List essential prime implicants

d$)$ Write the minimum SOP expression for the given truth table

e$)$ Write the minimum POS expression for the complement of the output $($Out$)$