‹ Back to the paper
The owner of a company pays bonus to his salesmen as per the criteria given below: If the…
The owner of a company pays bonus to his salesmen as per the criteria given below:
If the salesman works overtime for more than 4 hours but does not work on off days/holidays.
OR
If the salesman works when festival sales are on and updates showroom arrangements.
OR
If the salesman works on an off day/holiday when the festival sales are on.
The inputs are:
(In all the above cases 1 indicates yes and 0 indicates no.)
Output : X [1 indicates yes, 0 indicates no for all cases]
Draw the truth table for the inputs and outputs given above and write the POS expression for $X(O,F,H,U)$.
| INPUTS | |
|---|---|
| O | Works overtime for more than 4 hours |
| F | Festival sales are on |
| H | Working on an off day/holiday |
| U | Updates showroom arrangements |
Answer
Answer
AILet $X = O.H' + F.U + F.H$ (bonus is paid if: overtime>4hrs AND not on off day, OR festival sales on AND updates showroom, OR festival sales on AND working on off day/holiday).
Truth table (16 rows, inputs in the order O,F,H,U; verified with the boolean tool):
Maxterms (X=0) at rows 0,1,2,3,4,10,11, i.e. $X=\pi(0,1,2,3,4,10,11)$.
Canonical POS expression:
$X(O,F,H,U) = (O+F+H+U).(O+F+H+U').(O+F+H'+U).(O+F+H'+U').(O+F'+H+U).(O'+F+H'+U).(O'+F+H'+U')$
| O | F | H | U | X |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 1 | 1 | 0 |
| 1 | 1 | 0 | 0 | 1 |
| 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 |
From ISC 2019 Computer Science Paper 1, question 6(a).