GATE (Graduate Aptitude Test in Engineering) Computer Science & IT (CS) Set Theory & Algebra-Sets Study Material (Page 5 of 6)

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Binary Division and Restoring Division

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Binary Division

  • First, we must decide whether the divisor is less than or equal to the dividend.
  • For this, we must do a trial comparison/subtraction.
  • There are basically two types of division algorithms:
    • Restoring division
    • Non-restoring division
  • These are for positive numbers.
  • Negative numbers are handled the same way with the sign bits processed separately.
Binary Division

Restoring Division

  • I…

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IEEE 754 Arithmetic and Rounding

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  • IEEE 754 defines different rounding rules to use when calculating arithmetic results.
  • Arithmetic is generally performed by computing the result of an operation as if it were stored exactly (to infinite precision) , and then rounding it to fit in the format.
  • Apart from operations whose result already fits exactly into the format (such as adding 1.0 to 1.0) , the correct answer is generally somewhere between two representable numbers in the format.
  • The system then chooses one of these two numbers as the rounded result. It uses one of the following methods:

Round to Nearest

  • The…

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