Fixed Point Algorithm Computer Organization

Fixed Point Representation means that represents real numbers in a computer system, where the position of the decimal of the or binary point is fixed. This is in difference to floating point representation, where the position of the point can quotfloat.quot In fixed point representation, the number is split into an integer part and a fractional part.

In this chapter, we are going to learn different how an arithmetic operation of addition and subtraction is performed in computer hardware for fixed point numbers using electronic adders.

The Division of two fixed-point binary numbers in the signed-magnitude representation is done by the cycle of successive compare, shift, and subtract operations. The binary division is easier than the decimal division because the quotient digit is either 0 or 1.

Fixed-point numbers and their data types are characterized by their - word size in bits binary point and whether they are signed or unsigned The dynamic range of an N-bit number based on 2's- complement representation is between -2N-1 amp 2 N-1 - 1, or between -32,768 and 32,767 for a 16-bit system.

Floating Point Addition and Subtraction In floating point arithmetic, addition and subtraction are more complex than multiplication and division. This is because of the need for alignment. There are four phases for the algorithm for floating point addition and subtraction.

2 Fixed Point Representation of Numbers The simplest way to represent numbers in a computer is to allocate, for each number, enough space to hold N decimal digits, of which some lie before the decimal point and some lie after. For example, we might allocate 7 digits to each number, with 3 digits before the decimal point and 4 digits after.

To summarize, we have discussed the fixed point arithmetic unit. We looked at binary addition, subtraction, fast adders - carry look ahead adders and binary multiplication techniques. Web Links Supporting Materials Computer Organization, Carl Hamacher, Zvonko Vranesic and Safwat Zaky, 5th.Edition, McGraw- Hill Higher Education, 2011.

Explore the concepts of fixed point and floating point number representations, including their differences and applications in computing.

Fixed-point arithmetic In computing, fixed-point is a method of representing fractional non-integer numbers by storing a fixed number of digits of their fractional part. Dollar amounts, for example, are often stored with exactly two fractional digits, representing the cents 1100 of dollar.

The Binary Point fixed pt. vs. floating pt. Where do we put the binary point? Fixed Point one place, fixed for that design Interval remains the same for the entire real line