Floating Point Representations

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Floating Point Representations

• CDA 3101
• Discussion Session 02

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Question 1

• Converting the binary number
• 1100 0000 1101 1001 1001 1001 1001 10102
• to decimal, if the binary is single precision
  floating-point?

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Question 2

• Show the IEEE 754 binary representation for the
  floating-point number 0.110 in singleprecision
  and doubleprecision

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Question 3

• Convert the following single-precision numbers
  into decimal
• a. 0 11111111 0000000000000000000000
• b. 0 00000000 0000000000000000000010

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Question 4

• Consider the 80-bit extended-precision IEEE 754
  floating point standard that uses 1 bit for the
  sign, 16 bits for the biased exponent and 63 bits
  for the fraction (f). Then, write (i) the 80- bit
  extended-precision floating point representation
  in binary and (ii) the corresponding value in
  base-10 positional (decimal) system of
• the third smallest positive normalized number
• the largest (farthest from zero) negative
  normalized number
• the third smallest positive denormalized number
• that can be represented.