**| Computer Arithmetic : In Depth**

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## Number Representation

Conventional and oftentimes exotic methods of number representation can lead to performance gains in terms of simpler and faster circuits. While conventional methods are used extensively, the unconventional ones find application in special purpose digital circuits and systems.

Computer arithmetic deals with the hardware realization of arithmetic functions to support various computer architectures as well as with arithmetic algorithms for firmware or software implementation.

A major thrust of digital computer arithmetic is the design of hardware algorithms and circuits to enhance the speed of numeric operations. Thus computer arithmetic complements the architectural and algorithmic speedup techniques for high-performance computer architecture design and parallel processing.

Objectives:

- To be able to describe the core design elements of the Arithmetic and Logic Unit (ALUs) of top-of-the-line CPUs designed using high-performance parallel arithmetic circuits.
- At times we will also deal with slow bit-serial designs for embedded applications, where implementation cost and input/output pin limitations are of prime concern.
- It would be a mistake, though, to conclude that computer arithmetic is useful only to computer designers. We will see shortly that you can use scientific calculations more effectively and write programs that are more accurate and/or more efficient after a study of computer arithmetic.
- You will be able to render informed judgment when faced with the problem of choosing a digital signal processor chip for your project.

### Fixed Point Numbers

### References:

- Behrooz Parhami,
*Computer Arithmetic: Algorithms and Hardware Designs*, 2nd Edition, Oxford University Press, New York, 2010. - Henry S. Warren, Jr. ,
*Hacker’s Delight*, 2nd Edition, Addison-Wesley Professional, September 2012.