A ROM is to be used to implement the Boolean functions given below:
$${F_1}$$$$(A,\,B,\,C,\,D) = ABCD + \bar A\,\overline B \,\bar C\,\bar D$$
$${F_2}(A,\,B,\,C,\,D) = (A + B)(\bar A\, + \overline B + C)$$
$${F_3}(A,\,B,\,C,\,D) = \sum {13,15 + \sum {3,5} } $$

(a) What is the minimum size of the ROM required?

(b) Determine the data in each location of the ROM.

A Boolean function, F , given as sum of product (SOP) terms as F= $$\sum {} $$m(3,4,5,6) with A,B, and C as inputs. The function, F, can be expreeed on the Karnaugh's map shown below.

(1) What will be the minimized SOP expression for F?
(2) Implement this function on an 8 : 1 MUX.

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.