Page 663 - Computer science 868 Class 12
P. 663
(b) Given F(P, Q, R, S) = Π(1, 3, 4,5,6, 7, 9, 11, 12, 13, 14, 15)
(i) Reduce the above expression by using 4 variable Karnaugh map, showing the various groups (,i.e., octal, quads and pairs). [4]
Ans.
R+S R+S' R'+S' R'+S
P+Q 0 0 0 1 1 3 0 2
P+Q' 0 4 0 5 0 7 0 6
P'+Q' 0 12 0 13 0 15 0 14
P'+Q 0 8 0 9 0 11 1 10
Octet 1: M1.M3. M5.M7. M12.M13.M14.M15 = S’
Octet 2: M4.M5. M6.M7 .M12.M13.M14.M15 = Q’
Reduced POS expression : Q’.S’
(ii) Draw the Logic gate diagram of the reduced expression using gates. AND/OR gates. Assume that the variables and it’s
complements are available as inputs. [1]
Ans. Q' Q'.S
S'
Question 4. [5]
(a) The owner of a company pays the bonus to his salesmen as per the criteria are given below:
If the salesman sells product worth Rs 500000 per month but is not involved in advertising and marketing of the product.
OR
If the salesman works on an off day/holiday and is involved in advertising and marketing of the product.
OR
If the salesman works on an off day/holiday and when the festival sales are on.
The inputs are:
INPUTS
P Sells product worth Rs 500000 per month
F Works when festival sales are on
H Working on an off day/holiday
A Involved in advertising and marketing of the product
(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(P, F, H, A).
Ans.
P F H A X Maxterm
0 0 0 0 0 M0
0 0 0 1 0 M 1
0 0 1 0 0 M 2
0 0 1 1 1 M 3
0 1 0 0 0 M 4
0 1 0 1 0 M 5
0 1 1 0 1 M 6
0 1 1 1 1 M 7
1 0 0 0 1 M 8
1 0 0 1 0 M 9
1 0 1 0 1 M 10
1 0 1 1 1 M 11
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Sample Paper 661

