## Compute Slope and Bias

### What Is Slope Bias Scaling?

With slope bias scaling, you must specify the slope and bias of a number. The real-world value of a slope bias scaled number can be represented by:

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

`$slope=slopeadjustmentfactor×{2}^{fixedexponent}$`

### Compute Slope and Bias

```lower_bound = 999; upper_bound = 1000; is_signed = true; word_length = 16;```

To find the range of a `fi` object with a specified word length and signedness, use the `range` function.

`[Q_min, Q_max] = range(fi([], is_signed, word_length, 0));`

To find the slope and bias, solve the system of equations:

`lower_bound = slope * Q_min + bias `

`upper_bound = slope * Q_max + bias`

Rewrite these equations in matrix form.

`$\left[\begin{array}{c}\text{lower_bound}\\ \text{upper_bound}\end{array}\right]\text{=}\left[\begin{array}{cc}\text{Q_min}& \text{1}\\ \text{Q_max}& \text{1}\end{array}\right]\text{×}\left[\begin{array}{c}\text{slope}\\ \text{bias}\end{array}\right]$`

Solve for the slope and bias.

```A = double ([Q_min, 1; Q_max, 1]); b = double ([lower_bound; upper_bound]); x = A\b; format long g```

To find the slope, or precision, call the first element of the slope-bias vector, `x`.

`slope = x(1)`
```slope = 1.52590218966964e-05```

To find the bias, call the second element of vector `x`.

`bias = x(2)`
```bias = 999.500007629511```

Create a `numerictype` object with slope bias scaling.

`T = numerictype(is_signed, word_length, slope, bias)`
```T = DataTypeMode: Fixed-point: slope and bias scaling Signedness: Signed WordLength: 16 Slope: 1.5259021896696368e-5 Bias: 999.500007629511```

Create a `fi` object with `numerictype` `T`.

`a = fi(999.255, T)`
```a = 999.254993514916 DataTypeMode: Fixed-point: slope and bias scaling Signedness: Signed WordLength: 16 Slope: 1.5259021896696368e-5 Bias: 999.500007629511```

Verify that the `fi` object that you created has the correct specifications by finding the range of `a`.

`range(a)`
```ans = 999 1000 DataTypeMode: Fixed-point: slope and bias scaling Signedness: Signed WordLength: 16 Slope: 1.5259021896696368e-5 Bias: 999.500007629511```

Get trial now