Computer Arithmetic

In IEEE 754 double precision (64-bit), how many bits are the exponent and significand?

  1. A8-bit exponent, 55-bit significand
  2. B15-bit exponent, 48-bit significand
  3. C11-bit exponent, 52-bit significand
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Answer: C. 11-bit exponent, 52-bit significand

Double precision (FP64) uses 1 sign bit, 11 exponent bits and 52 significand bits, 64 in total. The exponent bias is 1023, covering roughly 10⁻³⁰⁸ to 10³⁰⁸, and the 53 bits of precision including the implied 1 correspond to about 15–16 decimal digits. Both fields are wider than in single precision, and it is the standard for scientific computing. An 8-bit exponent keeps the single-precision width while widening only the significand, which is not a standard format.

  • A. An 8-bit exponent is the single-precision width; double widens it.
  • B. A 15-bit exponent belongs to quadruple precision and similar.
  • C. Correct. 11-bit exponent and 52-bit significand.
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More Computer Arithmetic questions

  1. In IEEE 754 single precision, if the stored exponent field is 130, what is the actual exponent (power of two)?
  2. What is the effect of not storing the leading 1 of the significand (the hidden bit) in IEEE 754 normalized numbers?
  3. What is the hexadecimal bit pattern of decimal 1.0 in IEEE 754 single precision?
  4. Converting −6.25 to single precision, what is the sign–exponent–significand bit string written in hexadecimal?
  5. Which correctly describes representing decimal 0.1 as a binary floating-point number?