Question

A shopping mall allows customers to shop using the cash or credit card of any nationalised bank. In awards bonus points to their customers on the basis of criteria given below:

• The customer is an employee of the shopping mall and makes the payment using a credit card.
  OR
• The customer shops items which carry bonus points and makes the payment using a credit card with a shopping amount of less than  ₹10,000.
  OR
• The customer is not an employee of the shopping mall and makes the payment not through a credit card in cash for the shopping amount above ₹10,000/-

The inputs are:

INPUTS
C	Payment through a credit card.
A	Shopping amount in above  ₹10,000
E	The customer is an employee of the shopping mall.
I	Item carries a bonus point.

(In all the above cases, 1 indicates yes and 0 indicates no.) 

Output: X[1 indicates bonus point awarded, 0 indicates bonus point not awarded for all cases]

Draw the truth table for the inputs and outputs given above and write the POS expression for X(C, A, F, I).

Answer 1

Truth table

C	A	E	I	X	Maxterm
0	0	0	0	0	C + A + E + I
0	0	0	1	0	C + A + E + I'
0	0	1	0	0	C + A + E' + I
0	0	1	1	0	C + A + E' + I'
0	1	0	1	1
0	1	0	1	1
0	1	1	0	0	C + A' + E' + I
0	1	1	1	0	C + A' + E' + I'
1	0	0	0	0	C + A' + E' + I'
1	0	0	1	1
1	0	1	0	1
1	0	1	1	1
1	1	0	0	0	C' + A' + E + I
1	1	1	0	1	C' + A' + E + I'
1	1	1	0	1
1	1	1	1	1

POS Expression: F (C, A, E, I) = (C + A + E + I).(C + A + E + I’).(C + A + E’ + I).(C + A + E’ + I’).(C + A’ + E’ + I). (C + A’ + E’ + I’).(C’ + A + E + I).(C’ + A’ + E + I).(C’ + A’ + E + I’)

= ∏(0, 1, 2, 3, 6, 7, 8, 12, 13)