# Computer Arithmetic

This lecture does not take place at the moment. If you are interested, please inquire at the office.

Dates: -

Cut: 6 CP, 4 SWS

## Contents and goals

The lecture "Computer Arithmetic" aims at explaining how computers calculate, i.e. how arithmetic operations and functions are implemented using digital technology.

This is not only the basis for understanding how modern computers work, but also necessary for the design of application-specific hardware accelerators, which are becoming increasingly important in times of stagnating clock frequencies.

Different concepts, algorithms and structures are discussed and how they behave in their properties such as chip area, energy and performance.

The lecture is aimed at master students with a background in computer engineering or information and communication technology and with an interest in hardware implementations.

## Contents

Contents

• Number representation (fixed point numbers, floating point numbers, negative numbers, alternative number systems)
• Compressor Trees (Wallace tree, Dadda tree)
• Multiplication (Baugh-Wooley, Booth, higher radix multipliers)
• Division (Restoring/non-restoring division, SRT division)
• Function approximation (normalization, range reduction, polynomial approximations, rational approximations and splines, minimax, CORDIC algorithm, multipartite table methods)
• Floating point arithmetic (Addition/subtraktion, multiplication, division)
• Particularities for FPGAs

In addition to the lecture, the course (4 SWS, 6CP) also includes an exercise in which details of the lecture material can be deepened by means of concrete tasks.

Learning Objectives: The learner will be able to,

• evaluate the structure of arithmetic units on modern computers,
• apply different representations of numbers on computers,
• design arithmetic units for basic arithmetic operations and elementary functions.

## Literature and materials

The lecture builds on the book

Ercegovac, M. D., & Lang, T. (2004). Digital arithmetic. Morgan Kaufmann Publishers.

. Complementing these are the books.

Parhami, B. (2009). Computer Arithmetic - Algorithms and Hardware Designs. Oxford University Press.

Muller, J.-M. (2006). Elementary Functions (2nd ed.). Boston, MA: Springer Science & Business Media.

Used. Excerpts from these books as well as other materials will be handed out in the lecture .

## Proof of performance

The certificate of achievement will be given in the form of an oral examination. The exact modalities will be announced in the course.