Number Representation

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Question 1

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 2

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

• -256

• -128

• -127

• 0

Question 3

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 4

(1217)₈ is equivalent to

• (1217)₁₆

• (028F)₁₆

• (2297)₁₀

• (0B17)₁₆

Question 5

The octal number 326.4 is equivalent to

• (214.2)₁₀ and (D6.8)₎₁₆

• (212.5)₁₀ and (D6.8)₎₁₆

• (214.5)₁₀ and (D6.8)₎₁₆

• (214.5)₁₀ and (D6.4)₎₁₆

Question 6

Consider the following state diagram and its realization by a JK flip flop






The combinational circuit generates J and K in terms of x, y and Q.

The Boolean expressions for J and K are :

• (x⊕y)'and (x⊕y)'

• (x⊕y)'and x⊕y

• x⊕y and (x⊕y)'

• x⊕yand x⊕y

Question 7

The number of 1's in the binary representation of (3*4096 + 15*256 + 5*16 + 3) are: ISRO 2015

• 8

• 9

• 10

• 12

Question 8

The range of integers that can be represented by an n bit 2’s complement number system is: ISRO 2015

• - 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

Which of the given number has its IEEE-754 32 bit floating point representation as 0 10000000 110 0000 0000 0000 0000 0000

• 2.5

• 3.0

• 3.5

• 4.5

Question 10

Which of the following binary number is the same as its 2's complement?

• 1010

• 0101

• 1000

• 1001

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Computer Organization and Architecture