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Phrases Floating Point Representation PYQ

Phrases PYQ 2023
Suppose we have a 10-bit computer that uses 10-bit floating point computational unit (Float number uses IEEE floating-point arithmetic where a floating point number has 1 sign bit, 5 exponent bits, and 4 fraction bits). The representation for +∞ (plus infinity) is





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Solution

10-bit Floating Point: +∞ Representation

Format: The 10-bit floating point is structured as follows:

  • 1 bit for sign (S)
  • 5 bits for exponent (E)
  • 4 bits for fraction/mantissa (F)

IEEE Rule for +∞:

In IEEE floating-point format, +∞ is represented as:

  • Sign bit (S): 0
  • Exponent bits (E): all 1s → 11111
  • Fraction bits (F): all 0s → 0000

✅ Final 10-bit Representation: 0111110000


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