Scaling

Fixed-point numbers can be encoded according to the scheme

$real-world value = (slope \times integer) + bias$

where the slope can be expressed as

$slope = slope adjustment factor \times 2^{fixed exponent}$

The integer is sometimes called the stored integer. This is the raw binary number, in which the binary point assumed to be at the far right of the word. In Fixed-Point Designer™ documentation, the negative of the fixed exponent is often referred to as the fraction length.

The slope and bias together represent the scaling of the fixed-point number. In a number with zero bias, only the slope affects the scaling. A fixed-point number that is only scaled by binary point position is equivalent to a number in [Slope Bias] representation that has a bias equal to zero and a slope adjustment factor equal to one. This is referred to as binary point-only scaling or power-of-two scaling:

$real-world value = 2^{fixed exponent} \times integer$

$real-world value = 2^{-fraction length} \times integer$

Fixed-Point Designer software supports both binary point-only scaling and [Slope Bias] scaling.

Note

For examples of binary point-only scaling, see the Fixed-Point Designer Perform Binary-Point Scaling example.

For an example of how to compute slope and bias in MATLAB^®, see Compute Slope and Bias