# Documentation

## Cast from Doubles to Fixed Point

The purpose of this example is to show you how to simulate a continuous real-world doubles signal using a generalized fixed-point data type. Although simple in design, the model gives you an opportunity to explore many of the important features of the Fixed-Point Designer™ software, including

• Data types

• Scaling

• Rounding

• Logging minimum and maximum simulation values to the workspace

• Overflow handling

This example uses the `fxpdemo_dbl2fix` model. Open the model:

`fxpdemo_dbl2fix`

The sections that follow describe the model and its simulation results.

### Block Descriptions

In this example, you configure the Signal Generator block to output a sine wave signal with an amplitude defined on the interval `[-5 5]`. The Signal Generator block always outputs double-precision numbers.

The Data Type Conversion (Dbl-to-FixPt) block converts the double-precision numbers from the Signal Generator block into one of the Fixed-Point Designer data types. For simplicity, the size of the output signal is 5 bits in this example.

The Data Type Conversion (FixPt-to-Dbl) block converts one of the Fixed-Point Designer data types into a Simulink® data type. In this example, it outputs double-precision numbers.

### Simulations

The following sections describe how to simulate the model using binary-point-only scaling and [Slope Bias] scaling.

#### Binary-Point-Only Scaling

When using binary-point-only scaling, your goal is to find the optimal power-of-two exponent E, as defined in Scaling. For this scaling mode, the fractional slope F is 1 and there is no bias.

To run the simulation:

1. Configure the Signal Generator block to output a sine wave signal with an amplitude defined on the interval ```[-5 5]```.

1. Double-click the Signal Generator block to open the `Block Parameters` dialog.

2. Set the Wave form parameter to `sine`.

3. Set the Amplitude parameter to `5`.

4. Click .

2. Configure the Data Type Conversion (Dbl-to-FixPt) block.

1. Double-click the Dbl-to-FixPt block to open the `Block Parameters` dialog.

2. Verify that the Output data type parameter is `fixdt(1,5,2)`. `fixdt(1,5,2)` specifies a 5-bit, signed, fixed-point number with scaling `2^-2`, which puts the binary point two places to the left of the rightmost bit. Hence the maximum value is 011.11 = 3.75, a minimum value of 100.00 = -4.00, and the precision is (1/2)2 = 0.25.

3. Verify that the Integer rounding mode parameter is `Floor`. `Floor` rounds the fixed-point result toward negative infinity.

4. Select the Saturate on integer overflow checkbox to prevent the block from wrapping on overflow.

5. Click .

The Scope displays the real-world and fixed-point simulation results.

The simulation shows the quantization effects of fixed-point arithmetic. Using a 5-bit word with a precision of (1/2)2 = 0.25 produces a discretized output that does not span the full range of the input signal.

If you want to span the complete range of the input signal with 5 bits using binary-point-only scaling, then your only option is to sacrifice precision. Hence, the output scaling is `2^-1`, which puts the binary point one place to the left of the rightmost bit. This scaling gives a maximum value of 0111.1 = 7.5, a minimum value of 1000.0 = -8.0, and a precision of (1/2)1 = 0.5.

To simulate using a precision of 0.5, set the Output data type parameter of the Data Type Conversion (Dbl-to-FixPt) block to `fixdt(1,5,1)` and rerun the simulation.

#### [Slope Bias] Scaling

When using [Slope Bias] scaling, your goal is to find the optimal fractional slope F and fixed power-of-two exponent E, as defined in Scaling. There is no bias for this example because the sine wave is on the interval ```[-5 5]```.

To arrive at a value for the slope, you begin by assuming a fixed power-of-two exponent of -2. To find the fractional slope, you divide the maximum value of the sine wave by the maximum value of the scaled 5-bit number. The result is 5.00/3.75 = 1.3333. The slope (and precision) is 1.3333.(0.25) = 0.3333. You specify the [Slope Bias] scaling as [0.3333 0] by entering the expression `fixdt(1,5,0.3333,0)` as the value of the Output data type parameter.

You could also specify a fixed power-of-two exponent of -1 and a corresponding fractional slope of 0.6667. The resulting slope is the same since E is reduced by 1 bit but F is increased by 1 bit. The Fixed-Point Designer software would automatically store F as 1.3332 and E as -2 because of the normalization condition of 1 ≤ F < 2.

To run the simulation:

1. Configure the Signal Generator block to output a sine wave signal with an amplitude defined on the interval ```[-5 5]```.

1. Double-click the Signal Generator block to open the `Block Parameters` dialog.

2. Set the Wave form parameter to `sine`.

3. Set the Amplitude parameter to `5`.

4. Click .

2. Configure the Data Type Conversion (Dbl-to-FixPt) block.

1. Double-click the Dbl-to-FixPt block to open the `Block Parameters` dialog.

2. Set the Output data type parameter to `fixdt(1,5,0.3333,0)` to specify [Slope Bias] scaling as [0.3333 0].

3. Verify that the Integer rounding mode parameter is `Floor`. `Floor` rounds the fixed-point result toward negative infinity.

4. Select the Saturate on integer overflow checkbox to prevent the block from wrapping on overflow.

5. Click .

The Scope displays the real-world and fixed-point simulation results.

You do not need to find the slope using this method. You need only the range of the data you are simulating and the size of the fixed-point word used in the simulation. You can achieve reasonable simulation results by selecting your scaling based on the formula

`$\frac{\left(max_value-min_value\right)}{{2}^{ws}-1},$`

where

• max_value is the maximum value to be simulated.

• min_value is the minimum value to be simulated.

• ws is the word size in bits.

• 2ws - 1 is the largest value of a word with size ws.

For this example, the formula produces a slope of 0.32258.