# Floating Point/Floating Point Formats

## Floating-Point FormatsEdit

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-PrecisionEdit

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-PrecisionEdit

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.

## Extended-PrecisionEdit

## ReviewEdit

Format | Width | Precision | Exponent | Significand |
---|---|---|---|---|

Single | 32 bits | 23 bits | bits 30-23 | bits 22-0 |

Double | 64 bits | 52 bits | bits 62-52 | bits 51-0 |