What special value is represented when all exponent bits are 1 with all mantissa bits set to 0 in floating-point format?

When all exponent bits are 1 with all mantissa bits set to 0, it represents infinity, either positive or negative depending on the sign bit. This scenario is specifically designed to handle overflow situations where a calculation results in a value that exceeds the representable range of the floating-point format.

  • Sign Bit: The sign bit determines whether the infinity value is positive or negative. A sign bit of 0 represents positive infinity, while a sign bit of 1 represents negative infinity.
  • Exponent Bits: All exponent bits set to 1 indicate an overflow condition, where the result is too large to be represented within the finite range of the floating-point format.
  • Mantissa Bits: In the case of infinity, the mantissa bits are not used for representing fractional values since the exponent already indicates an overflow condition.

When a calculation or operation in a program results in a value that exceeds the maximum representable value in the floating-point format, the result is typically set to infinity to indicate that the computation has gone beyond the numerical limits of the format. This helps in handling exceptional cases and preventing numerical errors or inconsistencies in computations.

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