Lecture

Datapath Design: Mandelbrot & Fixed-Point

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In course

EE-334: Digital systems design

Students will acquire basic knowledge about methodologies and tools for the design, optimization, and verification of custom digital systems/hardware. They learn how to design synchronous digital circuits on register transfer level, analyse their timing a ...

Description

This lecture covers the design of datapaths for Mandelbrot set computation and fixed-point number representation in digital systems. It explains the Mandelbrot algorithm, VHDL arithmetic operations, Q-notation for fixed-point numbers, and the challenges of fixed-point arithmetic with integers.

Instructor

Andreas Peter Burg

Andreas Burg was born in Munich, Germany, in 1975. He received his Dipl.-Ing. degree in 2000 from the Swiss Federal Institute of Technology (ETH) Zurich, Zurich, Switzerland. He then joined the Integrated Systems Laboratory of ETH Zurich, from where he graduated with the Dr. sc. techn. degree in 2006. In 1998, he worked at Siemens Semiconductors, San Jose, CA. During his doctoral studies, he was an intern with Bell Labs Wireless Research for a total of one year. From 2006 to 2007, he held positions as postdoctoral researcher at the Integrated Systems Laboratory and at the Communication Theory Group of the ETH Zurich. In 2007 he co-founded Celestrius, an ETH-spinoff in the field of MIMO wireless communication, where he was responsible for the ASIC development as Director for VLSI. In January 2009, he joined ETH Zurich as SNF Assistant Professor and as head of the Signal Processing Circuits and Systems group at the Integrated Systems Laboratory. In January 2011, he became a Tenure Track Assistant Professor at the Ecole Polytechnique Federale de Lausanne (EPFL) where he is leading the Telecommunications Circuits Laboratory in the School of Engineering. In June 2018 he was promoted to the role of a Tenured Associate Professor. In 2000, Mr. Burg received the Willi Studer Award and the ETH Medal for his diploma and his diploma thesis, respectively. Mr. Burg was also awarded an ETH Medal for his Ph.D. dissertation in 2006. In 2008, he received a 4-years grant from the Swiss National Science Foundation (SNF) for an SNF Assistant Professorship. In his professional career, Mr. Burg was involved in the development of more than 25 ASICs. He is a member of the IEEE and of the European Association for Signal Processing (EURASIP). Research interests and expertise

Circuits and systems for telecommunications (wireless and wired)
Prototyping and silicon implementation of new communication technologies
Development of communication algorithms and optimization for hardware implementation
Low-power VLSI signal processing for communications and other applications
Digital integrated circuits
Circuits for image and video processing

Official source

Ontological neighbourhood

Mathematics

Analysis: Numerical analysis

Related concepts (32)

Fixed-point iteration

In numerical analysis, fixed-point iteration is a method of computing fixed points of a function. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is which gives rise to the sequence of iterated function applications which is hoped to converge to a point . If is continuous, then one can prove that the obtained is a fixed point of , i.e., More generally, the function can be defined on any metric space with values in that same space.

Floating-point arithmetic

In computing, floating-point arithmetic (FP) is arithmetic that represents subsets of real numbers using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. Numbers of this form are called floating-point numbers. For example, 12.345 is a floating-point number in base ten with five digits of precision: However, unlike 12.345, 12.3456 is not a floating-point number in base ten with five digits of precision—it needs six digits of precision; the nearest floating-point number with only five digits is 12.

Arithmetic

Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms, which are highly important to the field of mathematical logic today.

Arithmetic logic unit

In computing, an arithmetic logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers. This is in contrast to a floating-point unit (FPU), which operates on floating point numbers. It is a fundamental building block of many types of computing circuits, including the central processing unit (CPU) of computers, FPUs, and graphics processing units (GPUs).

Iterated function

In mathematics, an iterated function is a function X → X (that is, a function from some set X to itself) which is obtained by composing another function f : X → X with itself a certain number of times. The process of repeatedly applying the same function is called iteration. In this process, starting from some initial object, the result of applying a given function is fed again in the function as input, and this process is repeated. For example on the image on the right: with the circle‐shaped symbol of function composition.

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