A hypothetical six-bit system

A binary floating-point number format is characterized by its number of significant bits and its exponent range. The number of significant bits is called the precision. To keep things simple, it's helpful to look at a small number system. In a 6-significant-bit system, a typical number has the form , where the significand is presumed to be binary. The value of this number is . Represented this way, numbers are constrained by limits on the power-of-2 scale factor; an exponent ranging between and would be a reasonable (arbitrary) choice for such a number system. Numbers have algebraic sign as well: the negative of any representable value is itself representable. However, you can deduce most of the interesting properties of floating-point numbers from inspection of the positive values. Table 3 exhibits some positive representatives of this little number system.

Number Value Comment

Sample 6-bit floating-point values 		Maximum number
Maximum power of two
Largest number whose square doesn't overflow
Three
Next number greater than 1
One
Next number less than 1
Distance between 1 and its next upward neighbor
Distance between 1 and its next downward neighbor
Rounded value of 1/3
Next neighbor upward from smallest normal number
Smallest normal (or normalized) number
Largest subnormal (or denormalized) number
Smallest subnormal number

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