Floating Point/Floating Point Formats

Floating-Point Formats
There are 4 different formats of floating point number representation in the IEEE 754 standard:


 * Single-Precision:
 * Double-Precision:
 * Single, Extended-Precision:
 * Double, Extended-Precision:

Single-Precision
Single precision floating point numbers are 32 bits wide. The first bit (bit 31, the MSB) is a sign bit, the next 8 bits (bits 30-23) are the exponent, and the remaining 23 bits are for the significand. Note that even though 23 bits are stored for the significand, the precision($$p$$) is actually 24 bits. This is a trick made possible by a normalized floating point system with $$b = 2$$. The exponent is biased by 127, so that negative exponents can be expressed.

Double-Precision
Double-precision numbers are 64 bits wide. The MSB (bit 63) is the sign bit. The next 11 bits (bits 62-52) are the exponent, and the rest of the bits (bits 51-0) are for the significand. Again, the precision is actually 53 bits (not 52) because of the same normalization trick.