What is the internal representation of inf and NaN?

Question

A friend & I were debating how Inf's and NaN's are stored during lunch today.

Take Fortran 90 for example. 4-byte reals can obtain the value of Inf or NaN. How is this stored internally? Presumably, a 4-byte real is a number represented internally by a 32 digit binary number. Are Inf's and NaN's stored as 33 bit binary numbers?

Answer 1

Most floating point representations are based upon the IEEE standard, which has set patterns defined for Inf and NaN.

Answer 2

Specifically from Pesto's link:

The IEEE single precision floating point standard representation requires a 32 bit word, which may be represented as numbered from 0 to 31, left to right. The first bit is the sign bit, S, the next eight bits are the exponent bits, 'E', and the final 23 bits are the fraction 'F':

S EEEEEEEE FFFFFFFFFFFFFFFFFFFFFFF  
0 1      8 9                    31  

The value V represented by the word may be determined as follows:

• If E=255 and F is nonzero, then V=NaN ("Not a number")
• If E=255 and F is zero and S is 1, then V=-Infinity
• If E=255 and F is zero and S is 0, then V=Infinity
• If 0<E<255 then V=(-1)**S * 2 ** (E-127) * (1.F) where "1.F" is intended to represent the binary number created by prefixing F with an implicit leading 1 and a binary point.
• If E=0 and F is nonzero, then V=(-1)**S * 2 ** (-126) * (0.F) These are "unnormalized" values.
• If E=0 and F is zero and S is 1, then V=-0
• If E=0 and F is zero and S is 0, then V=0