DISCRETE MATHEMATICAL STRUCTURES II 1. Answer The following: a) Give an example of a relation which is reflexive and transitive but not symmetric. b) Find the value of A(2.2) where A(m, n) is defined below: A(0,n)=n+1 if n > 0 A(m,0) = A(m-1, 1) if m > 0 A(m,n)=A(m-1,A(m,n-1) if m,n>0 c) How many binary operations are possible on a set having n elements? d) What is a partially ordered set? e) Find the hamming distance between the code words 10010101 and 10011001 f) If <G, *> is a group having 17 elements with the identity element e then list all subgroups of the group <G, *>. g) Draw the Hasse diagram of the lattice (S, ≤) where S = {1,2,3.4,6,8,12,24} and for any elements a, b ∈ S, a ≤ b if and only if a divides b. 2. a) When do we say that a function is primitive recursive? Explain. b) Show that the function D(x) is primitive recursive where D(x) is the number of divisors of x. 3. a) Show that the set of all the invertible elements of a monoid form a group under the same operations as that of the monoid. b) State and prove the Lagranges theorem for groups. 4. a) Construct the decoding table for the group code C={(0,0,0,0,0,0),(0,0,1,0,1,1),(0,1,0,1,0,1),(0,1,1,1,1,0),(1,0,0,1,1,1),(1,0,1,1,0,0),(1,1,0,0,1,0),(1,1,1,0,0,1)} b) Prove that a code can correct all combinations of k or fewer errors if and only if the minimum distance between the any two code words is at least 2k+1. 5. a) What is the transitive closure of a relation? Find the transitive closure of the relation R = {(1,2),(2,3),(3,1),(1,3)} on the set S={1,2,3}. b) Show that there are only five distinct Hasse diagrams for partially ordered sets that contain three elements. 6. a) Define the terms Grammar and Language and illustrate with examples. b) Obtain a context free grammar which generates the language. L = { w l w contains twice as many 0s and 1s }. 7. a) When do we say that (B, *, ⊕, ', 0, 1) is a Boolean Algebra? List all properties of a Boolean Algebra. b) For the following Boolean expression give the circuit diagram representation and the Karnaugh map representation f = x'y'z + x'yz' + xyz'.
8. a) Explain the terms: Deterministic Finite state machine and Non-deterministic Finite state machine with examples. b) Design a deterministic finite state acceptor for sentences in { a, b } such that every a has a b immediately to its right.
MICRO PROCESSORS - I 1. (a) Distinguish between CPU and microprocessor (b) Does fetch and execute overlap occur in 8085 microprocessor. Justify your answer. (c) Draw the neat sketch showing demultiplexing of address bus and data bus in 8085 microprocessors. (d) How do you set Zero and CARRY flags of 8085? (e) What is the use of LOCK bar signal of 8086 microprocessor? (f) What is the number of T states in 8086 and 8088? (g) Give the instruction format of 8086 microprocessor. 2. (a) Write the complete specifications of 8085. Explain how Instruction Execution Process occurs in 8085 for any one of stack related instructions. (b) If hold and interrupt inputs of 8085 occur simultaneously. which one is accepted first? Justify your answer. 3. (a) Give the basic system timing diagram of 8085. (b) Write complete 8085 assembly language programming requirements and then write a program to find the GCD of two 8-bit numbers with a flowchart. 4. (a) Explain the complete interrupt structure of 8085. (b) Give the hardware and software for testing the interrupt logic of RST5.5 interrupt. 5. (a) Explain maximum mode and minimum mode interfaces of 8086. (b) Is the instruction format and instruction set of 8086 and 8088 same? Justify your answer by format and example instructions with detailed instructions. 6. (a) Write a program to transfer a string of characters from a given location to a destination location. Consider all the cases of overlapping. Assume the data necessary. (b) Write in brief about interrupts in 8086. 7. (a) Describe how BIU and EU interact for instruction execution with a suitable instruction sequence. (b) Write 8086 program with minimum number of instructions for resetting a flag register. 8. (a) What are Prefix instructions of 8086? Explain with examples. (b) Discuss about Coprocessor and Mutliprocessor environment with 8086 (c) Idents the addiess modes of each of the following 8086 instructions (i) MOV AH, [MP+2], (ii) MOV AH, 47H, (iii) MOV AH, [XRAY], (iv) MOV AH, [BP+SI], (v) MOV AH, TEMP[BS]
COMPUTER ORGANIZATION 1. (a) What is the arithmetic shift and how to identify the over flow? (b) What is firmware? (c) What is asynchronous transmission? (d) Define hit ratio? (e) What is handshaking? (f) Define index addressing mode? (g) What is write back procedure in cache memory? 2. (a) Show the hardware including logic gates for the control function that implements the statement xy1T0 + T1 + x1yT2 : A â&#x2020;? A+1 (b) Describe the register transfer language operation illustrating with one example? 3. (a) Describe the mechanism of an instruction fetching, decoding and execution using flow chart? (b) What are data manipulation instructions BASIC computer? Explain with examples. 4. (a) Compare hardware control and micro programmed control? (b) Show how nine bit micro operation field in a micro instruction can be divided into sub fields? Explain with an example. 5. (a) With flow charts explain how floating point addition is performed in a computer? (b) What are the functions performed by an I/O interface? Explain with an example. 6. (a) Compare and contrast isolated I/O and memory mapped I/O. (b) Why does I/O interrupt make more efficient use of the CPU? 7. (a) Explain the need of the memo hierarchy? (b) What is the associate memory and what kind of operation it is more suitable? 8. Write short notes on (i) Virtual Memory (ii) Instruction formats. (iii) DMA (iv) Memory Reference Instructions of BASIC Computer
OBJECT ORIENTED PROGRAMMING 1. Answer the following a) Write about Data Encapsulation. b) What is Dynamic binding? c) Give an example of an Inline function. d) When do you use Friend functions? e) What are Pure virtual functions? g) Write about Garbage collection. 2. a)Explain concepts of Object Oriented Programming. b) Discuss Operator overloading concept with complex number addition example. 3. a) Explain all kinds of inheritance with examples. b) Write a program using class templates to sort an array of integers and an array of float numbers. 4. a) What is polymorphism? Explain compile-time polymorphism. b) Write a program using virtual functions Your program contains two classes. Base class by name college, derived class by branch derived both will contain a function display() that displays their respective details. 5. a) Write a short note on i) Class diagrams ii) State chart diagrams. b) What is UML? Discuss interaction diagrams. 6. a) Discuss Exception Handling mechanism in C++. b) Write a program for file copying using file streams in C++. 7. a) Write a short notes on File Handling in Java. b) Write a program that implements an interface containing methods describing student information. 8. a) Define multi-threading. How threads are created in JAVA? b) What is a package? Write a program that shows scope of all kinds of variables inside and outside a package.
SYSTEMS PROGRAMMING 1. a) What is the difference in function between BALR and USING instructIons? (14) b) Explain Allocation. c) Define Macro Instruction. d) Differentiate in between pass and phase. e) Define Linkage Editor. f) Define Compiler. g) Differentiate in between simple RELOCATABLE and complex RELOCATABLE address constants. 2. a) Explain the role of Base Register. (5) b) Explain the role of Index Register. (5) c) Differentiate in between USING and DROP PSEUDO op codes. (4) 3. a) Give the design of single pass assembler. (9) b) Can we write an ALP without using USING OP CODE? How? what are the limitations. (5) 4. a) Give the design of single pass macro processor. (9) b) Explain the design of macro processor which can handle macro definitions within macros. (5) 5. a) Give the design part of Assembler corresponding to LTORG pseudo op code. (5) b) Give the design of Assembler corresponding to Extended MNEUMONICS. (4) c) Will the following divide 10 by 2? Justify. (5) L3,=f"10' D2,=f"2' ST3, 1000 6. a) Give the design of absolute loader. (7) b) Explain about Direct Linking Loader. (7) 7. a) Explain BSS loader. (8) b) At what point in time of each of the following loading schemes perform binding? (6) i. DLL, ii. BSS loader, iii. Dynamic binder, iv. Dynamic linking loader, v. Overlay, vi. Editor. 8. a) Explain Lexical Analysis in detail. (9) b) Differentiate in between TDP & BUP (5)
ELECTRONICS - II 1. (a) State the reasons for the increase in te bandwidth of an amplifier with feedback. (b) State the effect of voltage shunt on the input and output impedances of an amplifier with feedback. (c) Why RC oscillators cannot be used at radio frequencies? (d) Define "unity gain bandwidth" and "full power bandwidth" of an operational amplifier. (e) Why an operational amplifier is not used in open-loop condition for linear aplications? (f) What is "resolution time" of a binary circuit? (g) State the applications of monostable multivibrator. 2. (a) Prove the negative feed back in amplifiers reduces the gain and increases the signal-to- noise ratio. State the assumptions made in your derivations. (b) Find the voltage gain and the feedback factor of the feedback amplifier that produces 90 watts of power with 0.05% distortion. The local resistance is 8 ohms. The output stage supplies 90 watts to the 8 ohm load in the nonfeedback case with 4% harmonic distortion The input single for 90 watts of output is to be 1.0 volt with feedback. 3. (a) State and explain Barkhausen criterion for electronic systems to oscillate with feedback. (b) For the feedback amplifier shown in figure 1.0, determine Avf = νo / νs, Rif and Rof. Assume that the BJTs are identical and have hie =1.5 KΩ, hfe = 80, hre = hoe = 0 as parameters. -----DIAGRAM----4. (a) Explain why the oscillators incorporating crystals have excellent frequency stability. (b) Draw the circuit diagram of a Colpitt’s oscillator and explain how the Barkhausen criterion are satisfied. Derive the expressions for its frequency and condition for oscillations. 5. (a) Draw the circuit diagram of a stable differentiator using an operational amplifier and explain with necessary frequency characterstics how it can provide stable operation. (b) Realize Vo = 2V1 - 3V2 + 4V3 using an operational amplifier and resistances. (c) Explain with a neat circuit diagram how CMRR of an operational amplifier is measured. 6. (a) Realize (i) an inverting amplifier and (ii) a non-inverting amplifier to provide a gain of 20 and compare them with reference to their input impedances. (b) Design a monostable multivibrator of collector coupled to provide a delay pulse of 100 μ secs on application of trigger. Use BJTs having hfe = 80, VBE(sat) =0.7V, VCE(sat) = 0V, VBE(cutoff) = 0V. Assume supply voltages of ± 10V and IC(sat) =2 mA. Show the circuit diagram with all the component values and explain its operation with the waveforms seen at both the collectors and bases. 7. (a) Distinguish between symmetrical and non-symmetrical triggering of multivibrators. (b) Design a binary circuit of fixed bias using BJTs having hfe(mu) = 80, VBE(sat)= 0.7V, VCE(sat) =0.2V and VBE(cutoff) = 0V. Assume supply voltages of ±10 V are available. Take IC(sat) =5 mA. Show the circuit diagram with all the component values. Prove that when one transistor is "ON" the other Transistor is "OFF". 8. Write short notes on the following: (a) Crystal controlled oscillator. (b) Astable multivibrator. (c) Integrator circuit using an operational amplifier.4