Signals A,B,C,D and $$\overline D $$ are available. Using a single 8 - to - 1 multiplexer and no other gate, implement the Boolean function.

$$f(A,B,C,D) = B.C + A.B.\bar D + \bar A.\bar C.\bar D$$

A chemical reactor has three sensors indicating the following conditions:-
(1) Pressure (P) is low or high'
(2) Temperature (T) is low or high' and
(3) Liquid level (L) is low or high.

its has two controls - Heater (H) which is either on or off and inlet value (V) which is open or close. The controls are operated as per Table.

(a) Using the convertion High =1, Low = 0, On=1, Off=0, Open=1 and Closed=0, draw the Karnaugh maps for H and V.

(b) Obtain the minimal product of sums expressions for H and V.

(c) Realize the logic for H and V using two 4-input multiplexers with T and L as control inputs. Used T as MSB.