# Fixed point calculations

In computing, a fixed – point number representation is a real data type for a number that has a fixed number of digits after (and sometimes also before) the radix point Fixed – point number representation can be compared to the more complicated (and more computationally demanding) floating-point number representation. The use of fixed point data type is used widely in digital signal processing (DSP) and game applications, where performance is sometimes more important than precision. As we will see later, fixed point arithmetic is much faster than . The alternative, used by assembly language programmers for years, is to use fixed – point math that is executed using integer functions. Fixed – point math typically takes the form of a larger integer number, for instance bits, where the most significant eight .

While there is nothing particularly difficult about this subject, I found little documentation either in hardcopy or on the web. I therefore decided to develop this material and to . The following are fixed – point examples for multiplication and addition. The difference being the point bookkeeping required which is the same as addition.

For addition and subtraction . The idea behind fixed – point arithmetic is that you store the values multiplied by a certain amount, use the multiplied values for all calculus, and divide it by the same amount when you want the result. The purpose of this technique is to use integer arithmetic (int, long) while being able to represent fractions. Representing Fractional Numbers on Low-Cost DSPs.

To lower the cost of the implementation, many digital signal processors are designed to perform arithmetic operations only on integer numbers. To represent fractional numbers on these processors, we can use an implied binary point. Because the position of the binary point is entirely conceptual, the logic for adding and subtracting fixed – point numbers is identical to the logic required for adding and subtracting integers. Thus, when adding one half plus one half in Q3. Multiplication is little more than multiplies plus shifting.

Yes, there are some special cases one must watch for, but math is very fast compared to floats. So if you need fractional values and spee fixed . Certain Byte Craft Limited compilers can use fixed point values: fractional values between and of various precisions, and accumulator values with both small integer components and . A fixed point is a point that does not change upon application of a map, system of differential equations, etc. In particular, a fixed point of.

Linear Stability Analysis. Chaos and Integrability in Nonlinear Dynamics: An Introduction. In fact a large portion of processors do not even have hardware support for integer multiplication.

Fixed – point subtraction is equivalent to adding while using the two’s complement value . Once you know these well you can convert from hex-to-binary faster than a calculator and far beyond their digit display range. This necessitates software . A basic understanding of bytes, words, AD SUB and carry will also make this article far easier to digest.

Simple Fixed – Point Math. What is Fixed – Point maths? I recently needed to implement a simple fixed – point math library, and found that there were few good online resources on how to implement one and that many of the simple free implementations had subtle errors. I decided to distil out a few details I would have liked to have had .