Page 38 - Computer science 868 Class 12
P. 38
Draw the truth table for the inputs and outputs given above and write the POS expression for X(O, F, H, U). [ISC 2019]
Solution:
In the first statement, O=1 and H=0
Second statement is having F=1 and U=1
Third statement has H=1 and F=1
Let us draw the truth table and put 1 (true) in the final column X having the above combinations.
O F H U X Cardinal Number
0 0 0 0 0 0
0 0 0 1 0 1
0 0 1 0 0 2
0 0 1 1 0 3
0 1 0 0 0 4
0 1 0 1 1 5
0 1 1 0 1 6
0 1 1 1 1 7
1 0 0 0 1 8
1 0 0 1 1 9
1 0 1 0 0 10
1 0 1 1 0 11
1 1 0 0 1 12
1 1 0 1 1 13
1 1 1 0 1 14
1 1 1 1 1 15
For deriving POS expression, we multiply those maxterms which have 0 in their output column.
Thus, the final POS expression in the canonical form is:
(O+F+H+U).(O+F+H+U').(O+F+H'+U).(O+F+H'+U').(O+F'+H+U).(O'+F+H'+U).(O'+F+H'+U')
The expression in cardinal from is: π(0, 1, 2, 3, 4, 10, 11)
Example 2: A training institute intends to give scholarships to its students as per the criteria given below:
a. The student has an excellent academic record but is financially weak.
OR
b. The student does not have an excellent academic record and belongs to a backward class.
OR
c. The student does not have an excellent academic record and is physically impaired.
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