Computer Organization in GATE

GATE CS2010

1. P is a 16-bit signed integer. The 2’s complement of P is (F87B)₁₆. The 2’s Complement representation of 8*P is

(A) (C3D8)₁₆               (B) (187B)₁₆                 (C) (F878)₁₆                 (D) (987B)₁₆

GATE CS2009

2. (1217)₈ is equivalent to

(A) (1217)₁₆                 (B) (028F)₁₆                 (C) (2297)₁₀                 (D) (0B17)₁₆

GATE CS2008

3. Let r denote number system radix. The only value(s) of r satisfy the equation √(121)_r = (11)_r is/are

(A) decimal 10 (B) decimal 11              (C) Decimal 10 & 11    (D) any value>2

4. In the IEEE floating point representation the hexadecimal value 0x00000000 corresponds to

(A) The normalized value 2^-127               (C) The normalized value 2^-126

(C) The normalized value +0.                            (D) The special value +0

GATE CS2005

5. The range of integers that can be represented by an n bit 2’s complement number system is:

(A) -2^n-1 to (2^n-1-1)                                           (B) –(2^n-1-1) to (2^n-1-1)            

(C) -2^n-1 to 2^n-1                                                         (D) –(2^n-1+1) to (2^n-1-1)

6. The hexadecimal representation of 657₈ is:

(A) 1AF                       (B) D78                       (C) D71                       (D) 32F

Consider the following floating-point format.

                                   

7. The decimal number 0.239 x 2¹³ has the following hexadecimal representation (with out normalization and rounding off);

(A) 0D 24                    (B) 0D 4D                    (C) 4D 0D                   (D) 4D 3D

8. The normalized representation for the above format is specified as follows. The mantissa has an implicit 1 preceding the binary(radix) point. Assume that only 0’s are padded in while shifting a field.

The normalized representation of above number (0.239x2¹³) is:

(A) 0A 20                    (B) 11 34                     (C) 49 D0                    (D) 4A E8

GATE CS2004

9. Let A = 1111 1010 and B = 0000 1010 be two 8-bit 2’s complement numbers. Their product in 2’s complement is

(A) 1100 0100             (B) 1001 1100             (C) 1010  0101            (D) 1101 0101

10. What is the result of evaluating the following two expressions using three-digit floating point arithmetic with rounding?

            (113. + -111.) + 7.51

            113. +(-111. + 7.51)

(A) 9.51 and 10.0 respectively              (B) 10.0 and 9.51 respectively

(B) 9.51 and 9.51 respectively              (C) 10.0 and 10.0 respectively

11. If 73_x (in base x number system) is equal to 54_y (in base y number system), the possible values of x and y are

(A) 8,16                       (B) 10,12                     (C) 9,13                       (D) 8,11

GATE CS2003

12. Assuming all numbers are in 2’s complement representation, which of the following numbers is divisible by 11111011?

(A) 11100111              (B) 11100100              (C) 11010111              (D) 11011011

13. The following is a scheme for floating point number representation using 16 bits.

Let s,e, and m be the numbers represented in binary in the sign, exponent, and mantissa fields respectively, then the floating point number representation is:

(-1)^s (1+mx2^-9)2^e-31, if the exponent ≠ 111111

         0                    , otherwise

What is the maximum difference between two successive real numbers represent able in this system?

(A) 2^-40             (B) 2^-9                          (C) 2²²                         (D) 2³¹

 GATE CS2001

14. The decimal value 0.25

(A) is equivalent  to the binary value 0.1

(B) is equivalent to the binary valur 0.01

(C) is equivalent to the binary value 0.00111….

(D) cannot be represented precisely in binary

15.  The 2’s complement representation of the decimal value -15 is

(A) 1111                      (B) 11111                    (C) 111111                  (D) 10001

16.  Sign extension is a step in

(A) floating point multiplication

(B) signed 16 integer addition

(C) arithmetic left shift

(D) converting assigned integer from one size to another

17. Consider the following 32-bit floating –point representation scheme as shown in the formal below. A value is specified by 3 fields, a one bit sign field (with 0 for positive and 1 for negative values), a 24 bit fraction field (with the binary point being at the left end of the fraction bits), and a 7 bit exponent field (in excess-64 signed integer representation, with 16 being the base of exponentiation). The sign bit is the most significant bit.

           

(a) It is required to represent the decimal value -7.5 as a normalized floating point number in the given format. Derive the values of the various fields. Express your final answer in the hexadecimal.

(b) What is the largest values that can be represented using this format? Express your answer as the nearest power of 10.

GATE CS2000

18. The number 43 in 2’s complement representation is

(A) 01010101              (B) 11010101              (C) 00101011              (D) 10101011

19. Consider the values of A = 2.0x10³⁰, B = -2.0x10³⁰, C = 1.0, and the sequence

                        X:=A + B                     Y:= A + C

                        X:=X + C                     Y:= Y + B

Executed on a computer where floating point numbers are represented with 32 bits. The value for X and Y will be

(A) X=1.0, Y=1.0        (B) X=1.0, Y=0.0        (C) X=0.0, Y=1.0        (D) x=0.0, Y=0.0

GATE CS1999

20. Booth’s coding in 8 bits for the decimal numbers -57 is

(A) 0 – 100 + 1000      (B) 0 – 100 + 100 – 1  (C) 0–1+100–10+1     (D) 0 0 -10 + 100 – 1

21. Zero has two representations in

(A) Sign magnitude       (B) 1’s Complement     (C) 2’s Complement     (D) None of the above

GATE CS1998

22. The octal representation of an integer is 3428, if this were to be treated as an eight-bit integer is an 8085 based computer, its decimal equivalent is

(A) 226                        (B) -98                         (C) 76                          (D) -30

GATE CS1997

23. Given √(224)_r = (13)_r The value of the radix r is:

(A) 10                          (B) 8                            (C) 5                            (D) 6

GATE CS1996

24.  Booth’s algorithm for integer multiplication gives worst performance when the multiplier pattern is

(A) 101010…..1010                                        (B) 100000……0001

(C) 111111…..1111                                        (D) 011111……1110

25. Consider the following floating-point number representation.

The exponent is in 2’s complement representation and mantissa is in the sign magnitude representation. The range of the magnitude of the normalized numbers in this representation is

(A) 0 to 1                     (B) 0.5 to 1                  (C) 2^-23 to 0.5               (D) 0.5 to (1-2^-23)

GATE CS1995

26. What is the distance of the following code 000000, 010101, 000111, 011001, 111111?

(A) 2                            (B) 3                            (C) 4                            (D) 1

27. The number of 1’s in the binary representation of (3*4096+15*256+5*16+3) are:

(A) 8                            (B) 9                            (C) 10                          (D) 12

GATE CS1994

28. Consider n-bit(including sign bit) 2’s complement representation of integer number. The range of integer values, N, that can be represented is ____________≤N≤_________.

29. Following 7 bit single error correcting Hamming Coded message is received. (Figure below):

Determine if the message is correct (assuming that at most 1 bit could be corrupted). If the message contains an error find the bit which is erroneous an gives the correct message.

GATE CS1993

30. Convert the following numbers in the given bases into their equivalents in the desired bases.

A) (110.101)₂ = (x)₁₀

B) (1118)₁₀ = (y)_H

GATE CS1992

31. Consider a 3-bit error detection and 1-bit error correction hamming code for 4-bit date. The extra parity bits required would be ____________and the 3-bit error detection is possible because the code has a minimum distance of ____________.

32.  Consider addition in two’s complement arithmetic. A carry from the most significant but does not always correspond to an overflow. Explain, what is the condition for overflow in two’s complement arithmetic?

GATE CS1991

33. Consider the number given by the decimal expression: 16³ * 9 + 16² * 7 + 16 * 5 + 3

The number of 1’s in the unsigned binary representation of the number is ___________.