Number Representation

Question 21

Consider the equation (43)_x = (y3)₈ where x and y are unknown. The number of possible solutions is ________.

• 3
• 4
• 5
• 6

Question 22

(34.4)₈ × (23.4)₈ evaluates to:

• (1053.6)8

• (1053.2)8

• (1024.2)8

• None of these

Question 23

The 16-bit 2’s complement representation of an integer is 1111 1111 1111 0101; its decimal representation is   Note : This question was asked as Numerical Answer Type.

• 10
• 11
• -10
• -11

Question 24

Which of the following option is correct regarding number conversion from a base to another base?

• If a number has k digits in hex, then k/4 digits (bits) can have in binary.
• If a number has k digits in decimal, then roughly k/2 digits can have in binary.
• If a number has k digits base a, then roughly k*loga(b) digits can have in base b?
• None of the above

Question 25

The value of a float type variable is represented using the single-precision 32-bit floating point format IEEE-754 standard that uses 1 bit for sign, 8 bits for biased exponent and 23 bits for mantissa. A float type variable X is assigned the decimal value of −25.75. The representation of X in hexadecimal notation is

• 61CD0000
• C1640000
• C1CD0000
• C1CE0000

Question 26

What is the radix of the number if the solution to quadratic equation x^2 − 10x + 31 = 0 is x = 5 and x = 8?

• 10
• 8
• 5
• 13

Question 27

Consider the unsigned 8-bit fixed point binary number representation, below, b₇b₆b₅b₄b₃ ⋅ b₂b₁b₀ where the position of the binary point is between b₃ and b₂ . Assume b₇ is the most significant bit. Some of the decimal numbers listed below cannot be represented exactly in the above representation: (i) 31.500 (ii) 0.875 (iii) 12.100 (iv) 3.001 Which one of the following statements is true?

• None of (i), (ii), (iii), (iv) can be exactly represented

• Only (ii) cannot be exactly represented

• Only (iii) and (iv) cannot be exactly represented

• Only (i) and (ii) cannot be exactly represented

Question 28

The Octal equivalent of the binary number 1011101011 is :

• 7353
• 1353
• 5651
• 5657

Question 29

We consider the addition of two 2’s complement numbers b_n-1b_n-2...b₀ and a_n-1a_n-2...a₀. A binary adder for adding unsigned binary numbers is used to add the two numbers. The sum is denoted by c_n-1c_n-2...c₀ and the carry-out by c_out. Which one of the following options correctly identifies the overflow condition?

• A
• B
• C
• D

Question 30

In IEEE floating point representation, the hexadecimal number 0xC0000000 corresponds to

• -3.0
• -1.0
• -4.0
• -2.0