Please explain how each of these expansions is developed:

$$The function F

$=$

$$CD

$$

E

$+$

$$CDE

$+$

$$A

$$

D

$$

E

$+$

$$A

$$

B

$$

DE

$$

$+$

$$BCD is to be implemented in an FPGA which uses

$3$

$-$

variable lookup tables.

$($

a

$)$

$$Expand F about the variables A and B

$.$

$$ F

$=$

$($

b

$)$

$$Expand F about the variables B and C

$.$

$$ F

$=$

$($

c

$)$

$$Expand F about the variables A and C

$.$

$$ F

$=$

$($

d

$)$

$$Use your preceding answers to implement F using only three

$3$

$-$

variable lookup tables and a

$4$

$-$

to

$-$

$1$

$$MUX$.$ Give the truth tables for the lookup tables. Attach files of your circuit implementation and your truth table