Arithmetics and Codes

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Digital Design

Synopsis:

Students will learn various data representations used in digital devices and will be able to design units realizing arithmetic operations and coders and decoders for error detection and correction.

Requirements:

Design of combinational and sequential logic circuits at the gate level, linear algebra basics.

Syllabus of lectures:

1. Error control codes - basic principles.

2. Linear codes.

3. Cyclic codes.

4. Burst error correction.

5. Multi-error correction.

6. Number systems, addition and subtraction.

7. Codes for signed number representation.

8. Multiplication.

9. Division.

10. Floating point.

11. Elementary functions.

Syllabus of tutorials:

1. Finite fields.

2. Polynomials over finite field.

3. Linear codes and error corrections.

4. Cyclic codes.

5. Burst error correction.

6. Multi-error correction.

7. TEST.

8. Number systems and codes.

9. Adders and subtractors.

10. Multiplication and multipliers.

11. Floating point representation.

Study Objective:

Circuits realizing arithmetic operations belong to fundamental components of computers and digital devices in general. In the module, algorithms for basic and advanced arithmetic operations will be presented that are suitable especially to be implemented using logic circuits. The goal is to present various ways to detect or correct individual errors and burst errors in data stored into memories or transmitted via channels.

Study materials:

Pluháček, A. ''Projektování logiky počítačů''. Praha: ČVUT, 2003. ISBN 80-01-02145-9.

Hlavička, J., Racek, S., Golan, P., Blažek, T. ''Číslicové systémy odolné proti poruchám''. Praha: ČVUT, 1992. ISBN 80-01-00852-5.

Adámek, J. ''Kódování''. Praha: SNTL, 1989.

Parhami, B. ''Computer Arithmetic: Algorithms and Hardware Designs''. Oxford University Press, 2009. ISBN 0195328485.

Koren, I. ''Computer Arithmetic Algorithms (2nd edition)''. A. K. Peters, 2001. ISBN 1568811608.

Muller, J. M. ''Elementary Functions: Algorithms and Implementation (2nd edition)''. Birkhäuser Boston, 2005. ISBN 0817643729.

Moreira, J. C., Farrell, P. G. ''Essentials of Error-Control Coding''. Wiley, 2006. ISBN 047002920X.

Lin, S., Costello, D. J. ''Error Control Coding (2nd Edition)''. Prentice Hall, 2004. ISBN 0130426725.

Note:

Further information:

https://courses.fit.cvut.cz/MI-AAK/

No time-table has been prepared for this course

The course is a part of the following study plans: