What would the smallest positive value of an IEEE 24-bit float be?

floating-point ieee-754 floating-point-precision 24-bit
Ky. picture Ky. · Sep 19, 2012 · Viewed 9.9k times · Source

The smallest positive value of an IEEE-754 32-bit float is 2^−149 and that of a 16-bit float is 2^-14. If the IEEE-754 standardized a 24-bit float, what would its smallest positive value be?

Excuse me if this is explicitly documented somewhere, but I wasn't able to find it in searches.

If you want to know about the practicality, this will be used to fit four floating-point values of varying precision into 64 bits for use in a memory-deficient system.

Answer

Stephen Canon picture Stephen Canon · Sep 19, 2012

IEEE-754 doesn't actually answer this question; it doesn't provide for standardizing a 24-bit format, and the usual formulas for determining the number of significand bits in a floating-point format break down for small widths.

That said, the most natural choice would be to have seven exponent bits and sixteen explicit significand bits, which makes the smallest positive normal number 2^-62.

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