# MCA CS-07 PROJECT Discrete Mathematics

**MCA CS-07 PROJECT Discrete Mathematics**

Course Code : CS-07

Course Title : Discrete Mathematics

Assignment Number : MCA(4)-07/Project/04

Maximum Marks : 15

Last date of Submission : 30th October, 2004

This is a Project Assignment. There are three questions in this. Answer all questions. You may use illustrations and diagrams to enhance explanations.

Question 1: Design the following circuits, clearly explaining the steps involved:

i) A binary majority function is generated in a circuit when the output is 1 if the binary input variables have more 1’s than 0’s and otherwise the output is 0. The circuit should use only NAND gates.

ii) A circuit that accepts a three-bit number and generates an output binary number equal to the square of the input number.

(5 marks)

Question 2: Use Karnaugh map representation to find minimal product-of-sums

expression for each of the following Boolean functions:

i) f (x,y,z,w) = Σ (1,2,4,9,10,11,14,15)

ii) f (x,y,z,w) = Σ (7,8,9,10,14,15)

(3 marks)

Question 3: Translate the following English arguments into Propositional Calculus (PC) and Decide in PC, for each argument, whether it is a valid argument or not :

i) If the parliament refuses to enact new laws, then the strike will not be over unless it lasts more than one year and the president of the firm resigns.

Conclusion: If either the parliament enacts new laws or the strike is not over then the strike lasts more than one year.

ii) No second-hand car dealer buys a second–hand car for his family. Some people who buy second-hand cars for their families are absolutely dishonest.

Conclusion : Some absolutely dishonest people are not second-hand car dealers.

(7 marks)