Computer Organization I Recitation

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Computer Organization IRecitation
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IEEE Standard 754 Floating Point Numbers

• presents numbers as a base number and an
  exponent.
• 123.456 is represented as 1.23456 102.
• In hexadecimal, 123.abc is represented as 1.23abc
  162.

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IEEE Standard 754 Floating Point Numbers

• Single Precision
• A floating point value represented in a single 32
  bit word
• Double Precision
• A floating point value represented in a two 32
  bit word

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IEEE Standard 754 Floating Point Numbers

• The value is
• S sign 0 denotes a positive number 1 denotes
  a negative number.
• Bias 127 for single precision and 1023 for
  double precision

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IEEE Standard 754 Floating Point Numbers

• Single Precision
• Double Precision

Fraction
Exponent
S
8 bits
23 bits
1 bit
Fraction
S
Exponent
1 bit
52 bits
11 bits
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IEEE Standard 754 Floating Point Numbers

• Representing in IEEE 754
• Represent the number in binary format
• Convert into scientific form
• Convert into
• where bias 127or 1023
• Put the values in the appropriate positions.

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IEEE Standard 754 Floating Point Numbers

• Convert -0.75 in single precision
• Binary of -0.75 is -0.11
• In scientific notation it is -1.1X 2(-1)
• Putting in the general form
• it becomes
• 1 01111110 10000000000000000000000

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IEEE Standard 754 Floating Point Numbers

• 3.38
• Show the IEEE 754 binary representation for the
  number 20.5

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IEEE Standard 754 Floating Point Numbers

• 3.30
• Given the bit pattern 1010 1101 0001 0000 0000
  0000 0000 0010
• What does it present, assuming it is
• A twos complement integer
• An unsigned integer
• A single precision floating point number?