Fixed Point Operations in VHDL : Tutorial Series Part 1

     You must have heard about library named fixed_pkg.In terms of complexity this library can be placed some where between integer math and floating point maths.I have decided to write a series of tutorials about the usage of fixed_pkg library.The library helps to handle fractional numbers with ease.
The library can be downloaded from here.

In the first part of this tutorial, I will give an introduction about the library and the new data types available for use.

How to use this library in your module?
Add the following two lines to your code(the place where you usually add the libraries):

library ieee_proposed;
use ieee_proposed.fixed_pkg.all;

What are the new data types available in the package?
     FIXED_PKG defines two new data types.They are UFIXED ( for unsigned fixed point) and SFIXED (for signed fixed point).

How to declare signals?
Say you want a fixed point unsigned signal with 'a' bits for decimal part and 'b' bits for fractional part,then you can declare them as follows:

signal example : ufixed( a-1 downto -b);
--an example
signal example : ufixed (3 downto -4);

Here the signal 'example' has 4 bits for decimal part and 4 bits for fractional part.
example = 9.75 = "1001.1100" or simply example ="10011100".

For signed numbers we use "sfixed" while declaring the signals.Signed numbers are stored as 2's complement format.

--an example for signed fixed point type.
signal example : sfixed(4 downto -4);

     Here the signal 'example' has 5 bits of decimal part and 4 bits for fractional part.
example = -9.75 = "101100100".This is got by taking 2's complement of binary value of 9.75.The MSB bit '1' indicates the number as negative.

If you declare the signal as sfixed and still store a positive value(say 9.75) then it has the same kind of storage format as ufixed.

--an example
signal example : sfixed(4 downto -4);
--If 'example' contains 9.75 then it is storage as "01001.1100".

     Remember that you declare the signals with sufficient width so that values are get stored correctly.If the width is not enough then the signal may get rounded off.