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

$$V\approx \tilde{V}=SQ+B,$$

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.

• 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.

Related Topics

• Scaling
• Data Types and Scaling in Digital Hardware