Problem $1,30$ Points $-4$ parts

Design a circuit to control an automatic sliding door system, similar to those found at a grocery store's entrance. It is a double$-$door, and, under normal circumstances, will open if there is a person in front of the door. When the store is closed, a switch will be set such that the doors do not open. A switch will be set if manual operation of the doors is necessary. An emergency switch will open the doors, for the purpose of evacuation.

The input variables are:

$P-$ active high $-$ from the door sensor$,$ active indicates detection of a person in front of the door

$H-$ active high $-$ from a control switch, assertion indicates manual operation of the door

C $-$ active high $-$ a control switch, active indicates door should remain closed $($e$.$g$.$ store closed$)$

$E-$ active low $-$ from the power override switch, active indicates emergency where doors are open

The output variable is:

D$-$St $-$ active high $($i$.$e$.0=$ closed; $1=$ open$)-$ to the door activation motor, when asserted will open the door.

a$)(5$ points$)$ Fill out the function table provided below.

b$)(5$ points$)$ Using the Function Table you have just created, write the function D$-$St as a canonical SOP $($standard sum of products, no simplification$).$

c$)(10$ points$)$ Provide the reduced equation for D$-$St$.$ NOTE: you may use any method, but K$-$Map template is provided for ease of use.

d$)(10$ points$)$ Draw the circuit diagram for the system design $($based on the answer to part c$,$ above$).$

$\backslash$table$[[$PHCE$,$D$-$St$],[0000,],[0001,],[0010,],[0011,],[0100,],[0101,],[0110,],[0111,],[1000,],[1001,],[1010,],[1011,],[1100,],[1101,],[1110,],[1111,]]$

$D-St=q,$

please include do not care conditions