IEEE 754 standard.
2 types:
- single precision
- double precision
Single precision
Uses bits.
- sign bit - bit
- exponent - bit
- mantissa - bit
Sign bit
if positive or zero. if negative.
Exponent
Exponent field range - . In this range is defined for normal
numbers. and are reserved for subnormal, infinite, signed zeros and
NaN.
To support negative exponents, we subtract (half of ) from this
range. . This range is the representable range.
Mantissa
In scientific notation, the part that doesn’t contain the base and the power.
In binary scientific notation, there will always be exactly one bit before
the dot. So we don’t include that one.
Double precision
Uses bits.
- sign bit - bit
- exponent - bit
- mantissa - bit
Sign bit
if positive or zero. if negative.
Exponent
Exponent field range - . In this range is defined for
normal numbers. and are reserved for subnormal, infinite, signed
zeros and NaN.
To support negative exponents, we subtract (half of ) from this
range. . This range is the representable range.
Mantissa
In scientific notation, the part that doesn’t contain the base and the power.
In binary scientific notation, there will always be exactly one bit before
the dot. So we don’t include that one.