10. Find, underline and translate the other examples in the text.

11. Find the mistakes and correct the sentence.

1. It is much difficult to measure changes which affected counting styles.

2. This is all the most important as there has been very little research.

3. As an example, diamond is about 4-5 times the hardest than corundum.

4. Round off your answer so it has only as much significant digits the quantity which contains the lesst number of significant digits.

5. Are double digits too much to expect?

12. Translate the following sentences into Russian.

1. The stored bits in the illustration represent the binary numeral 1011, which is 11 in decimal numbers.

2. The only data recorded is the delta-the differences that occur in the frames trailing the original reference frame.

3. When you work with decimal numbers, you need to understand the difference between trailing zeros and leading zeros, as well as how they affect the value of the number.

4. Computers are designed to manipulate digital data-specific values are expressed in real numbers.

5. When adjacent digits in a digit string are touching the recognition task becomes particularly challenging.

13. Translate the following sentences into English.

1. В теории вычислительных машин и систем, а также в теории формального языка нульстрока представляет собой однозначную строку в нуль длины.

2. В информатике, плавающая запятая описывает способ представления и обработки действительных чисел.

3. Биективная, взаимно однозначная система счисления с основанием b использует различные числа b для того чтобы представить все натуральные числа.

4. Метод сжатия данных является одной из самых важных областей и инструментов современной информатики.

5. В математике, нулевой байт в конце строки это последовательность 0 в десятичном представлении числа.

SPEAKING SECTION

5. Answer the following questions.

1. What is a numeral system?

2. Can you explain the reason when decimal representation is used for the rational or real numbers, the representation is no longer unique?

3. What kind of types of numerical systems you can name?

4. What is the most commonly used system of numerals nowadays? Why?

5. Is there any difference between positional and additive systems? If yes, what?

5. Topics for discussion.

1. Numeral Systems.

2. The History of Numbers.

3. Ancient Counting Systems.

5. Prepare a presentation on the topic being discussed.

REFERENCES, USEFUL LINKS AND FURTHER READING

REFERENCES AND FURTHER READING

1. ‘How computer works’, by Ron White, 2008, pp.8-9.

2. Georges Ifrah. The Universal History of Numbers : From Prehistory to the Invention of the Computer, Wiley, 1999. ISBN 0-471-37568-3.

   1. Knuth. The Art of Computer Programming. Volume 2, 3rd Ed. Addison-Wesley. pp.194–213, "Positional Number Systems".

3. J.P. Mallory and D.Q. Adams, Encyclopedia of Indo-European Culture, Fitzroy Dearborn Publishers, London and Chicago, 1997.

4. Hans J. Nissen, P. Damerow, R. Englund, Archaic Bookkeeping, University of Chicago Press, 1993, ISBN 0-226-58659-6.

5. Denise Schmandt-Besserat, How Writing Came About, University of Texas Press, 1992, ISBN 0-292-77704-3.

6. Claudia Zaslavsky, Africa Counts: Number and Pattern in African Cultures, Lawrence Hill Books, 1999, ISBN 1-55652-350-5.

APPENDIX

Base names

1 - unary

2 - binary

3 - ternary / trinary

4 - quaternary

5 - quinary / quinternary

6 - senary / heximal / hexary

7 - septenary / septuary

8 - octal / octonary / octonal / octimal

9 - nonary / novary / noval

10 - decimal / denary

11 - undecimal / undenary / unodecimal

12 - dozenal / duodecimal / duodenary

13 - tridecimal / tredecimal / triodecimal

14 - tetradecimal / quadrodecimal / quattuordecimal

15 - pentadecimal / quindecimal

16 - hexadecimal / sexadecimal / sedecimal

17 - septendecimal / heptadecimal

18 - octodecimal / decennoctal

19 - nonadecimal / novodecimal / decennoval

20 - vigesimal / bigesimal / bidecimal

21 - unovigesimal / unobigesimal

22 - duovigesimal

23 - triovigesimal

24 - quadrovigesimal / quadriovigesimal

26 - hexavigesimal / sexavigesimal

27 - heptovigesimal

28 - octovigesimal

29 - novovigesimal

30 - trigesimal / triogesimal

31 - unotrigesimal

(...repeat naming pattern...)

36 - hexatridecimal / sexatrigesimal

(...repeat naming pattern...)

40 - quadragesimal / quadrigesimal

41 - unoquadragesimal

(...repeat naming pattern...)

50 - quinquagesimal / pentagesimal

51 - unoquinquagesimal

(...repeat naming pattern...)

60 - sexagesimal

(...repeat naming pattern...)

64 - quadrosexagesimal

(...repeat naming pattern...)

70 - septagesimal / heptagesimal

80 - octagesimal / octogesimal

90 - nonagesimal / novagesimal

100 - centimal / centesimal

(...repeat naming pattern...)

110 - decacentimal

111 - unodecacentimal

(...repeat naming pattern...)

200 - bicentimal / bicentesimal

(...repeat naming pattern...)

210 - decabicentimal

211 - unodecabicentimal

(...repeat naming pattern...)

300 - tercentimal / tricentesimal

400 - quattrocentimal / quadricentesimal

500 - quincentimal / pentacentesimal

600 - hexacentimal / hexacentesimal

700 - heptacentimal / heptacentesimal

800 - octacentimal / octocentimal / octacentesimal / octocentesimal

900 - novacentimal / novacentesimal

1000 - millesimal

2000 - bimillesimal

(...repeat naming pattern...)

10000 - decamillesimal

1Skimming means to get a general idea of what a text is about. Read the first paragraph (the introduction) and the last paragraph (the conclusion). Then read the first and last sentences of the other paragraphs.

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