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.

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

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

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