- scientific notation for a floating-point number

符号・仮数・指数の底・指数 - binary number format
- the significand is usually a fraction
- the exponent is a signed integer

- problem: how many bits are assigned to the exponent and fraction?
number range / precision tradeoff

*Example:**m*_{e}=7*,**m*_{f}=24*m*_{e}=9*,**m*_{f}=22 - the significand is usually a fraction
- bias (excess) representation of the exponent:
- if
,
where
*e*_{min},*e*_{max}> 0then

- if
,
where
- normalized floating-point numbers
- for normalized numbers, the leftmost digit of the significand is nonzero

- hidden bit
- for base 2 floating-point numbers, 1 is the only nonzero digit
- an extra bit of accuracy in the significand can be gained by not storing this bit

- for base 2 floating-point numbers, 1 is the only nonzero digit