Arithmetics and Codes

Přednášející:

Alois Pluháček (gar.)

Cvičící:

Alois Pluháček (gar.)

Předmět zajišťuje:

katedra číslicového návrhu

Anotace:

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.

Požadavky:

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

Osnova přednášek:

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 adders.

7. Subtraction and negative number representations.

8. Multiplication.

9. Division.

10. Floating point.

11. Elementary functions.

12. Convolution codes and turbo codes.

Osnova cvičení:

1. Unconventional applications of number systems

2. Finite fields.

3. Polynomials over finite field.

4. Linear codes and error corrections.

5. Cyclic codes and burst corrections.

6. Multi-error correction.

7. Test.

8. Number systems and codes.

9. Adders and subtractors.

10. Multiplication and multipliers.

11. Floating point representation.

12. Spare seminar, assessment.

Cíle studia:

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 (including elementary mathematical functions) 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.

Studijní materiály:

1. Parhami, B. Computer Arithmetic: Algorithms and Hardware Designs. Oxford University Press, 1999. ISBN 0195125835.

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

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

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

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

Poznámka:

Rozsah=prednasky+proseminare+cviceni2p+1c, Prednasejici: doc. Ing. Alois Pluháček CSc.

Rozvrh na zimní semestr 2011/2012:

Rozvrh není připraven

Rozvrh na letní semestr 2011/2012:

Rozvrh není připraven

Předmět je součástí následujících studijních plánů:

• Computer Security, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (povinný předmět oboru)
• Design of Digital Systems, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (povinný předmět oboru)
• Master Informatics, Presented in English - Version for Students who Enrolled in 2010 (VO)
• Master Informatics, Presented in English - Version for Students who Enrolled in 2011 (VO)
• Master Informatics, Presented in English - Version for Students who Enrolled in 2012 (VO)
• Computer Security, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět oboru)
• Design of Digital Systems, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět oboru)