# II/IV B.Tech (Regular/Supplementary) DEGREE EXAMINATION. Discrete Mathematical Structures. Answer ONE question from each unit.

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1 14CS IT302 November,2016 II/IV B.Tech (Regular/Supplementary) DEGREE EXAMINATION Common for CSE & IT Discrete Mathematical Structures (4X12=48 Marks) 1. Answer all questions (1X12=12 Marks) a (Pv~P) is a tautology or contradiction? b Give the generating function A(X) for the sequence a n =(n+1)? c Give a relation that is antisymetric but not asymetric. d What is a TOSET? e Give the principle of Mathematical Induction? f State the Euler s theorem? g Give the chromatic number for Cycle if the length is even? h What is meant by Bi partite graph? i What is the difference between tree and graph? j Show that 3 and 24 integers are congruent modulo 7? k Define Hamiltonian graph. l Define Euler s Circuit. UNIT I 2.a Show that: [P v (P^Q) P] (Using truth table) 2.b Show that: [P v (~P^Q) P vq](using rules of propositions) 3.a Prove (or) Disprove the validity of the following argument. Every living thing is a Plant or animal. Davids dog is alive and it is not a plant. All animals have hearts. Hence, David s dog has a heart. 3.b Write any three methods of proof of an implication with an example. UNIT II 4.a Use Principle of Mathematical Induction to Prove that : 6 n n+1 is divisible by 43 for each +ve integer n. 4.b Use Principle of Mathematical Induction to Prove that for all Integers: n 4, 3 n > n 3. 5.a Find the coefficient of X 25 in (X 2 +X 3 +X 4 +X 5 +X 6 ) 7 5.b i)involving 1, 2,or 3 letters and1, 2, 3, or 4 digits if the letters must occur together. ii) In how many ways can the committee of 5 teachers and 4 students be chosen from 9 Teachers and 15students be formed if teacher A refuses to serve if student B is on the committee? 6.a UNIT III Computethe coefficients of d r X r = 6.b Solve the recurrence relation:a n =2 a n/2 +(n-1) for n 2, where a 1 =0. 7.a Find the transitive closure of the relation R={(a,b)(b,c)(c,c)(a,d)(c,d)(d,a)} using warshall s algorithm 7.b Draw Hasse diagram of the poset ({1,2,3,4,6,12}, ).Check whether it is a Lattice or not.

2 UNIT IV 8.a What is meant by Isomorphism? Determine whether the following graphs G and HIsomorphic or not? 14CS IT b What is meant by coloring of a Graph?.What is the Chromatic no of complete graph K n 9.a State and prove Euler s formula. 9.b Show that every Chain is a Lattice.

3 14CS IT 303 November,2016 II/IV B.Tech (Regular/Supplementary) DEGREE EXAMINATION Common for CSE & IT Digital Logic Design (4X12=48 Marks) 1. Answer all questions (1X12=12 Marks) a. Convert decimal 43 into hexadecimal and BCD number system. b. What is the reduced form for the Boolean function A+AB+ABC? c. Which of the logic gates are used to realize the all possible combinational logic functions? d. What is the maximum number of prime-implicants for n-variable Boolean function? e. Write the expression borrow (M) and difference (N) for half subtractor with X and Y inputs. f. Develop AND gate with 2 by 1 multiplexer g. The present output Q n of an edge triggered JK flip flop is logic 0. If J = 1, then what is the value of Q n+1 h. Write the excitation table for SR flip flop. i. What are the applications of shift registers? j. Compare synchronous and asynchronous counters. k. How many minimum number of MOS transistors required to make a dynamic RAM cell? l. What is the full form of EEPROM UNIT I 2.a Find X value in the following problems (i) (52) BCD = ( X ) 8 (ii) (425) 10 = ( X ) BCD (iii) (10111) gray = ( X ) 2 2.b Implement EX-NOR gate function using only NAND gates 3.a Convert the following Boolean equation into canonical POS and SOP form f(a,b,c) = ) 3.b Simplify the following Boolean function using 4-varaiable K-map and implement the simplified function with NOR gates only. f(a,b,c,d) = m(0,1,2,4,5,7,11,15) UNIT II 4.a Minimize the following Boolean function using tabulation method f(a,b,c,d) = m(0,1,2,8,9,15,17,21,24,25,27,31) 4.b Implement the following sum of min-term equation by using a decoder and logic gates. f(a,b,c) = m(0,2,3,7) 5.a Design a binary to gray code converter. 5.b Implement 16 X 1 multiplexer using 4 X 1 multiplexers

4 14CS IT 303 UNIT III 6.a What is race-around condition in JK flip-flop? Explain how it is eliminated in Master Slave JK flip-flop 6.b Obtain characteristic equation of X-Y flip flop whose truth table as shown below X Y Q n Q n 1 0 Q n a Design a mod-6 synchronous counter using JK flip flops 7.b Explain about state tables, state diagrams, state reduction and assignment. UNIT IV 8.a Distinguish between PLA and PAL. 8.b Design a 4-bit binary up and down ripple counter. 9.a Classify shift registers and explain any two with neat diagram 9.b Implement the following Boolean function using ROM F 1 (a,b) = m(1,2 ) F 2 (a,b) = m(0,1,3)

6 CS/IT a Explain how unconditional branches affect pipeline. 7.b With examples explain how branch prediction reduces the effect of branch instructions on pipelining. UNIT IV 8.a List and explain interrupt priority schemes. 8.b Write about DMA bus arbitration approaches. 9.a With neat timing diagrams explain synchronous and asynchronous buses. 8M 9.b Explain about USB I/O interface in detail. 4M

7 CS/IT213 November, 2016 II/IV B.Tech (Supplementary) DEGREE EXAMINATION Common for CSE & IT Computer Graphics (4X12 = 48 Marks) 1 Answer all the following (12X1 = 12 Marks) a) What is a pixel? b) What is DDA? c) What is Antialiasing? d) Define coherence properties. e) Distinguish between window port and view port? f) Define viewing transformation. g) What is a spline? h) What are the important properties of Bezier Curve? i) Define scaling in 3D transformation. j) What are the steps in animation sequence? k) What are 2 types of parallel projection? l) Define frame. UNIT I 2. a) Write design of CRT with two display procedures. b) Compare the random scan display and raster scan display. 3.a) Explain flood fill algorithm. b) Explain midpoint algorithm for line generation. UNIT II 4.a) Write a 2x2 transformation matrix for each of the following rotations about the origin. I. Counter clockwise by π II.Counter clockwise by π/2 III. Counter clockwise by 5π/2. b) Write about rotation transformation. 5.a)Explain two dimensional viewing functions b) Explain Sutherland Hodgeman polygon Clipping algorithm. UNIT III 6.a) Explain Spline representation. b) Briefly explain curved lines and surfaces. 7.a) A triangle is defined by 3 vertices A(0,1,1) B(2,1,0) c(1,2,1) find the final coordinates after it is rotated by 45 around a line joining the points (1,1,1) and (0,0,0). b) Explain 3D translation transformation with homogeneous coordinates. UNIT IV 8.a) Explain in detail 3D Clipping. b) Explain about view volume. 9.a) Classify different types of animation languages. b) Explain key frame systems.

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