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15.2.1 Binary Floating-point Representation

Although floating-point representations vary from machine to machine, the most commonly encountered representation is that defined by the IEEE 754 Standard. An IEEE-754 format value has three components:

The value of the number is then s * 2^e. The first bit of a non-zero binary significand is always one, so the significand in an IEEE-754 format only includes the fractional part, leaving the leading one implicit. The significand is stored in normalized format, which means that the first bit is always a one.

Three of the standard IEEE-754 types are 32-bit single precision, 64-bit double precision and 128-bit quadruple precision. The standard also specifies extended precision formats to allow greater precisions and larger exponent ranges.