Number Representation

Question 51

The octal representation of an integer is (342)₈. If this were to be treated as an eight bit integer in an 8085 based computer, its decimal equivalent is

• 226
• -98
• 76
• -30

Question 52

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

• 10
• 8
• 5
• 6

Question 53

Following floating point number format is given f is a fraction represented by a 6-bit mantissa (includes sign bit) in sign magnitude form e is a 4-bit exponent (includes sign hit) in sign magnitude form n= (f, e) = f, 2^e  is a floating point number. Let A= 54.75 in decimal and B= 9.75 in decimal. a). Represent A and B as floating point numbers in the above format. b). Show the steps involved in floating point addition of A and B. c). What is the percentage error (upto one position beyond decimal point) in the addition operation in (b)?

Question 54

Booth\'s algorithm for integer multiplication gives worst performance when the multiplier pattern is

• 101010 .........1010
• 100000 .........0001
• 111111 .........1111
• 011111 .........1110

Question 55

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)

• a

• b

• c

• d

Question 56

IEEE Standard 754 floating point is the most common representation today for real numbers on computers. The diagram below shows these parts are stored in memory: The IEEE 754 standard includes special cases for numbers that are difficult to represent, such as 0 because it lacks an implicit leading 1. Consider the following situations for IEEE Standard 754 floating point: Which of the following option is not correct?

• Code-1 represented number Zero
• Code-2 represented +/- Denormalized number
• Code-3 represented +/- Infinity
• Code-4 represented number Zero

Question 57

Let m=(313)₄ and n=(322)₄. Find the base 4 expansion of m+n.

• (635)₄
• (32312)₄
• (21323)₄
• (1301)₄

Question 58

A computer with 32 bit word size uses 2s complement to represent numbers. The range of integers that can be represented by this computer is

• –2³² to 2³²

• –2³¹ to 2³²-1

• –2³¹ to 2³¹-1

• –2³¹-1 to 2³²-1

Question 59

Let M = 11111010 and N = 00001010 be two 8 bit two’s complement number. Their product in two’s complement is

• 11000100

• 10011100

• 10100101

• 11010101

Question 60

Convert the octal number 0.4051 into its equivalent decimal number.

• 0.5100098
• 0.2096
• 0.52
• 0.4192