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:

$$real\text{-}worldvalue=(slope\times integer)+bias$$

$$slope=slopeadjustmentfactor\times {2}^{fixedexponent}$$

Start with the endpoints that you want, signedness, and word length.

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.

$$\left[\begin{array}{c}\text{lower\_bound}\\ \text{upper\_bound}\end{array}\right]\text{=}\left[\begin{array}{cc}\text{Q\_min}& \text{1}\\ \text{Q\_max}& \text{1}\end{array}\right]\text{\xd7}\left[\begin{array}{c}\text{slope}\\ \text{bias}\end{array}\right]$$

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