#1,091 – Subnormal Floating Point Numbers

32-bit binary floating point numbers are normally stored in a normalized form, that is:


where d is the fractional part of the mantissa, consisting of 23 binary digits and e is the exponent, represented by 8 bits.

In this form, the minimum allowed value for e is -126, which is stored in the 8-bit exponent as a value of 1.  Because the leading 1 is implicit, this means that the  minimum positive floating point value is:


We could use the 8-bit value of 0 in the exponent to represent an exponent of -127, but that would only gain us a single power of two, or one more value that we could store.

Instead, a value of of 0 stored in the 8-bit exponent is a signal to drop the leading 1 in the mantissa.  This allows storing a set of much smaller numbers, known as subnormal numbers, of the form:


We can now use all 23 digits in the mantissa, allowing us to store numbers as low as 2^-149.


About Sean
Software developer in the Twin Cities area, passionate about .NET technologies. Equally passionate about my own personal projects related to family history and preservation of family stories and photos.

One Response to #1,091 – Subnormal Floating Point Numbers

  1. Pingback: Dew Drop – May 7, 2014 (#1771) | Morning Dew

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