Number Representation

Question 1

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 2

The decimal value 0.5 in IEEE single precision floating point representation has

• fraction bits of 000…000 and exponent value of 0
• fraction bits of 000…000 and exponent value of −1
• fraction bits of 100…000 and exponent value of 0
• no exact representation

Question 3

The smallest integer that can be represented by an 8-bit number in 2’s complement form is

• -256
• -128
• -127
• 0

Question 4

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

• (C3D8)₁₆
  

• (187B)₁₆
  

• (F878)₁₆
  

• (987B)₁₆
  

Question 5

(1217)₈ is equivalent to

• (1217)₁₆
• (028F)₁₆
• (2297)₁₀
• (0B17)₁₆

Question 6

In the IEEE floating point representation, the hexadecimal value 0 × 00000000 corresponds to

• the normalized value 2^-127
• the normalized value 2^-126
• the normalized value +0 
• the special value +0 

Question 7

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 −14.25. The representation of X in hexadecimal notation is

• C1640000H
• 416C0000H
• 41640000H
• C16C0000H

Question 8

The range of integers that can be represented by an n bit 2\'s complement number system is

• - 2^{n - 1} to (2^{n - 1} - 1)
• - (2^{n - 1} - 1) to (2^{n - 1} - 1)
• - 2^{n - 1} to 2^{n - 1}
• - (2^{n - 1} + 1) to (2^{n - 1} + 1)

Question 9

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

• 8, 16
• 10, 12
• 9, 13
• 8, 11

Question 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) 

• 9.51 and 10.0 respectively
• 10.0 and 9.51 respectively
• 9.51 and 9.51 respectively
• 10.0 and 10.0 respectively