Fixed-Point Numbers in Simulink

Simulink^® data type names must be valid MATLAB^® identifiers with less than 128 characters. The data type name provides information about container type, number encoding, and scaling.

You can represent a fixed-point number using the fixed-point scaling equation

$V \approx \tilde{V} = S Q + B,$

where

V is the real-world value.
$\tilde{V}$ is the approximate real-world value.
S = F2^E is the slope.
F is the slope adjustment factor, where F is a value in the range [1.0, 2.0).
E is the fixed power-of-two exponent.
Q is the stored integer.
B is the bias.

Fixed-Point Data Type and Scaling Notation

The following table provides a key for various symbols that appear in Simulink products to indicate the data type and scaling of a fixed-point value.

Symbol	Description	Example
Container Type
`ufix`	Unsigned fixed-point data type	`ufix8` is an 8-bit unsigned fixed-point data type
`sfix`	Signed fixed-point data type	`sfix128` is a 128-bit signed fixed-point data type
`fltu`	Scaled Doubles override of an unsigned fixed-point data type (`ufix`)	`fltu32` is a scaled doubles override of `ufix32`
`flts`	Scaled Doubles override of a signed fixed-point data type (`sfix`)	`flts64` is a scaled doubles override of `sfix64`
Number Encoding
`e`	10^	`125e8` equals `125*(10^(8))`
`n`	Negative	`n31` equals `-31`
`p`	Decimal point	`1p5` equals `1.5` `p2` equals `0.2`
Scaling Encoding
`S`	Slope	`ufix16_S5_B7` is a 16-bit unsigned fixed-point data type with `Slope` of `5` and `Bias` of `7`
`B`	Bias	`ufix16_S5_B7` is a 16-bit unsigned fixed-point data type with `Slope` of `5` and `Bias` of `7`
`E`	Fixed exponent (2^) A negative fixed exponent describes the fraction length	`sfix32_En31` is a 32-bit signed fixed-point data type with a fraction length of `31`
`F`	Slope adjustment factor	`ufix16_F1p5_En50` is a 16-bit unsigned fixed-point data type with a `SlopeAdjustmentFactor` of `1.5` and a `FixedExponent` of `-50`
C, c, D, or d	Compressed encoding for Bias Note If you pass this symbol to the `slDataTypeAndScale` function, it returns a valid `fixdt` data type.	No example available. For backwards compatibility only. To identify and replace calls to `slDataTypeAndScale`, use the Check for calls to slDataTypeAndScale Model Advisor check.
T or t	Compressed encoding for Slope Note If you pass this symbol to the `slDataTypeAndScale`, it returns a valid `fixdt` data type.	No example available. For backwards compatibility only. To identify and replace calls to `slDataTypeAndScale`, use the Check for calls to slDataTypeAndScale Model Advisor check.

Fixed-Point Numbers in Simulink

Fixed-Point Data Type and Scaling Notation

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