Question

Question 3: Answer the following short question   

Questions 3(a): A milk producing factory has four sensors,

First sensor (A) checks the color of milk and if the color is good it turns ON.

Second sensor (B) checks if the label (sticker) of company is correctly pasted and turns ON.

Third sensor (C) checks if the cap of bottle is properly closed and turns ON.

Fourth sensor (D) checks if the weight of the bottle is correct and turns ON if it is correct.

The bottle is shipped when any three of the four sensors are turned ON.

1. Draw the truth table for when the bottle will be shipped. [2 Marks]

2. Use K-map to reduce the function. [2 Marks]

X= ABC+ ABC+ABC+ABC

pls answer q3 3a and 3b

Answer 1

a.

Truth table for the condition of when the bottle will be shipped is as follows:

T in A, B, C and D represents That the corresponding sensor is ON and F represents that the corresponding sensor is OFF.

T in SHIP means that the bottle will be shipped under that condition and F represents that the bottle will not ship.

A	B	C	D	SHIP
T	T	T	T	T
T	T	T	F	T
T	T	F	T	T
T	T	F	F	F
T	F	T	T	T
T	F	T	F	F
T	F	F	T	F
T	F	F	F	F
F	T	T	T	T
F	T	T	F	F
F	T	F	T	F
F	T	F	F	F
F	F	T	T	F
F	F	T	F	F
F	F	F	T	F
F	F	F	F	F

b.

K-MAP to reduce the function.

The given equation is X=ABC+ABC+ABC+ABC

Using the identity, A+A=A, the given equation is reduced to X=ABC

Now, to minimise the equation using K-MAP we have to get the min terms, which is obtained as follows:

X=ABC(D+D')

X=ABCD+ABCD'

Plotting the min terms in K-MAP, we get:

Therefore, the given equation is finally reduced to

X=ABC