## Scaling

Fixed-point numbers can be encoded according to the scheme

$$\text{real-worldvalue}=\left(\text{slope}\times \text{integer}\right)+\text{bias}$$

where the slope can be expressed as

$$\text{slope}=\text{slopeadjustmentfactor}\times {\text{2}}^{\text{fixedexponent}}$$

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:

$$\text{real-worldvalue}={2}^{\text{fixedexponent}}\times \text{integer}$$

or

$$\text{real-worldvalue}={2}^{\text{-fractionlength}}\times \text{integer}$$

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