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Design of a 32-bit Arithmetic Unit based on Composite Arithmetic and its Implementation on a Field Programmable Gate Array

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Pinkiewicz, T (1999) Design of a 32-bit Arithmetic Unit based on Composite Arithmetic and its Implementation on a Field Programmable Gate Array. Honours thesis, University of Tasmania.

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Abstract

As we advance into the new century, computers of the future will require new
techniques for arithmetic operations, which take advantage of the modern technology
and yield accurate results. Floating-point arithmetic has been in use for nearly forty
years, but is plagued with inaccuracies and limitations which necessitate introduction
of a new concept in computer arithmetic, called Composite Arithmetic. Composite
Arithmetic combines fixed-point and floating-point arithmetic into one integrated
concept where numbers are automatically assigned the right form. This negates the
need for differentiating between integer and real numbers in programming languages
and allows for better accuracy in calculations. The concept has two main forms:
exact and inexact. The exact form deals with integers and rational numbers, while
inexact form deals with numbers that cannot be represented exactly. To develop and
implement such concept in hardware, tools are needed that will allow for easy design
and re-design process, at a low cost. A device that meets these requirements is a
Field Programmable Gate Array. This electronic device provides quick and easy way
of designing the system and then implementing it by downloading data to the device.
It can then be tested and reprogrammed as desired, without the need for a new
device. This thesis is an attempt to design and implement Simple Composite
Arithmetic Machine (SCAM), which will be capable of performing operations on
exact numbers (rational and integer numbers). The core of the research is Composite
Arithmetic Unit, which contains operations like Multiply, Divide, Add and Subtract.
It also can find Greatest Common Divisor and cast out common factors of two
numbers. The CAU is controlled using Control Unit and Feedback Unit, and results
are stored in the Register Unit. The SCAM is therefore a basic microarchitecture that
will form a basis for further research in this field.

Item Type: Thesis (Honours)
Keywords: Composite Arithmetic, Fixed-point, Floating-point, Field Programmable Gate Arrays, FPGA
Publisher: Honours thesis, University of Tasmania
Date Deposited: 10 Jan 2007
Last Modified: 18 Nov 2014 03:12
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