# Why do the data become zero when using the function fi?

`fm = get_fimath();`

idx = fi(1,0,1,0,fm);

a = (idx+fi(2,0,2,0,fm))*fi(1/3,0,16,17,fm);

k = fi(a,0,17,0,fm)

function fm = get_fimath()

fm = fimath('RoundingMethod', 'Floor',...

'OverflowAction', 'Wrap',...

'ProductMode','FullPrecision',...

'MaxProductWordLength', 128,...

'SumMode','FullPrecision',...

'MaxSumWordLength', 128);

end

This code is generated when using the Matlab Coder . I want to know why is k equal to zero? Is it because of division 1/3?

# ANSWER

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It's just like scientific notation

is the short answer to "Why FractionLength can be bigger than WordLength?".

The long answer is the following.

The concept of a binary-point is very useful for initial understanding of fixed-point types. Similarly, the concept of a decimal-point is useful for understanding values beyond integers. But using decimal-points becomes very cumbersome for very big or very small numbers. To make it easy to represent very big or very small values, scientific notation is super valuable.

`verySmallNumber = 3e-200;`

veryBigNumber = 7e123;

In essence, this notation breaks the value into two parts, a mantissa and an integer exponent for the given base.

Y = mantissa .* 10.^exponent

Fixed-point follows the same concept except that

- base is 2
- mantissa must be an integer
- exponent is fixed, i.e. it is part of the variables type and does not change for the life of the variable

Y = intMantissa .* 2^FixedExponent

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