Path: utzoo!attcan!uunet!ginosko!gem.mps.ohio-state.edu!tut.cis.ohio-state.edu!ucbvax!agate!apple!motcsd!hpda!hpcupt1!hpisod2!decot
From: decot@hpisod2.HP.COM (Dave Decot)
Newsgroups: comp.org.ieee
Subject: Re: IEEE Standard for Floating Point
Message-ID: <20120002@hpisod2.HP.COM>
Date: 8 Oct 89 00:44:05 GMT
References: <1861@jato.Jpl.Nasa.Gov>
Organization: Hewlett Packard, Cupertino
Lines: 59

IEEE Standard for Binary Floating-Point Arithmetic, ANSI/IEEE Std 754-1985.

To quote from a draft version (presumably the same as the final version):

	Numbers in the single and double formats are composed of three fields:

		A 1-bit sign s.
		A biased exponent e = E + bias
		A fraction f = .b b ....b
				 1 2     p-1

	...

	A 32-bit single format number X is divided as shown in Figure 1. The 
	value v of X is inferred from its constituent fields thus:

	(1) If e = 255 and f != 0, then v is NaN [not-a-number] regardless of
	    s.
	(2) If e = 255 and f = 0, then v = (-1)^s * infinity.
	(3) If 0 < e < 255, then v = (-1)^s * 2^(e-127) * (1.f).
	(4) If e = 0 and f != 0, then v = (-1)^s * 2^(-126) * (0.f)
	    (denormalized numbers).
	(5) If e = 0 and f = 0, then v = (-1)^s * 0 (zero).

	Figure 1. Single Format

	 1    8            23		...widths	
	+-+--------+----------------+
	|s|   e    |        f       |
	+-+--------+----------------+
	   msb  lsb msb          lsb	...order
	
	"msb" means "most significant bit"
	"lsb" means "least significant bit"

	...

	A 64-bit double format number X is divided as shown in Figure 2. The 
	value v of X is inferred from its constituent fields thus:

	(1) If e = 2047 and f != 0, then v is NaN [not-a-number] regardless of
	    s.
	(2) If e = 2047 and f = 0, then v = (-1)^s * infinity.
	(3) If 0 < e < 2047, then v = (-1)^s * 2^(e-1023) * (1.f).
	(4) If e = 0 and f != 0, then v = (-1)^s * 2^(-1022) * (0.f)
	    (denormalized numbers).
	(5) If e = 0 and f = 0, then v = (-1)^s * 0 (zero).

	Figure 2. Double Format

	 1    11            52		...widths	
	+-+--------+----------------+
	|s|   e    |        f       |
	+-+--------+----------------+
	   msb  lsb msb          lsb	...order

(I've used "^" to signify exponentiation and "*" to signify multiplication)

Hope this helps!