User:Seema.andc/Question papers

B.Sc (Hons) Mathematics (Computer Mathematics) Paper XVII and XVIII (V) Max : marks 30

Q-1 Attempt any three parts (a)(i) Show that conjunction distributes over disjunction.

(ii) Define joint denial ↓ and prove that the three connectives ~ ,^ and v may be                  in terms of connective  ↓. (iii) Test whether [ ( p ↔ q ) ^ q → p is a tautology or not. (b) (i) Algebraically check the validity of the equation ( X+ Y ) ( Y+ Z ) ( X + Z ) = ( X + Y ) ( X + Z ) ( Y + Z )

(ii) Find the dual of the function F = (X + 1). (Y + Z ) Are the function and its dual logically equivalent.

(iii) evaluate ( ( AB) ↓ C ) Ө ( C ↓ ( D  Ө A ) ) For A= 1,B = 0,C = 1, D =1.

(c) Construct the four- variable karnaugh map for F(W,X,Y,Z) = ∑ (0,2,,5,7,8,9,11) + d (3,4,13,14) (i) Find the complete sum (ii) Find a minimal sum OR      (d) Construct the four- variable karnaugh map for F(A,B,C,D) = ∑ (1,3,7,9,13,14,15) + d (5,6,12) (i)Find the complete sum (ii)Find a minimal sum Q-2 Attempt any two parts (a)  (i) Convert (237.14) 8 in to binary number then convert it in to hexadecimal.

(ii) What is the range of numbers that can be represented using n-bit system in        signed magnitude representation. (iii) Calculate -47 + (- 75) using 8 bit binary numbers (sign + 7 bits) in (a)	One’s complement representation (b)	Two’s complement representation.

(b) (i) Why is two’s complement preferred over one’s complement. (ii) Divide 10011 by 11010 using restoring division.

(iii) Multiply 101.0101 by 1101.011.

(iv)Give an example to show that overflow in digital computers may produce an              Erroneous sign reversal.

( c)     (i) Express TEACHER in ASCII code.

(ii) using 9’s complement and 10’s complement subtract – 4563 from – 2137.

(iii) Divide (1000.101)2 by (101.01)2 using non restoring division. Q-3 (a) Attempt any two parts. (i) Determine which of the following are valid identifiers: (1)	Record number (2)	123-45-6789           (ii) Identify errors if any from the following control structure:- VAR result : real; --                 WHILE  result > 0 DO                  BEGIN ---                 END; (iii) What type of expressions are supported by Pascal?How do they differ. (b) (i)Write a program to calculate the factorial of an integer quantity.

(ii) Identify error if any. PROCEDURE SUM (a,b,c: REAL); VAR SUM : REAL BEGIN SUM = a+b+c; END;

(c) (i) What is the purpose of WHILE –DO structure.

(ii) Identify errors if any, from the following expressions:- (i) SUM DIV 0.005         (ii) ‘100’+’27’+’440’ (iii) What is the final value of x in the following program segment. x:= 3.76; x:= (x + 0.05)* 10 i:= trunc(x) x:= i;                        x:=x/10