Floating Point/Floating Point Formats There are 4 different
formats of floating point number representation in the IEEE 754
standard: - Single, Extended-Precision - Double, Extended-
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() is actually 24 bits.
This is a trick made possible by a normalized floating point
system with . The exponent is biased by 127, so that negative
exponents can be expressed. 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.
|Single||32 bits||23 bits||bits 30-23||bits 22-0| |Double||64
bits||52 bits||bits 62-52||bits 51-0|