Эксперт по сдаче вступительных испытаний в ВУЗах
Additional tasks to unit “Numerals”
Task 1. Answer the questions:
- What is the difference between numerals and numbers?
- What numbers are named after certain nationalities?
Task 2. Read the text below and check your answers.
Numbers should be distinguished from numerals, the symbols used to represent numbers. Boyer showed that Egyptians created the first ciphered numeral system. Greeks followed by mapping their counting numbers onto Ionian and Doric alphabets. Number five can be represented by digit «5» or by the
Roman numeral «V». An important development in the history of numerals was the development of a positional system, like modern decimals, which have many advantages, such as representing very large numbers with only a few symbols. Roman numerals require extra symbols for larger numbers.
Task 3. Make a list of different numeral systems. Why are there different numeral systems? Where are they used?
Task 4. Enlarge your list if necessary after reading the text below.
The simplest numeral system is the
unary numeral system, in which every
natural number is represented by a corresponding number of symbols. If the symbol / is chosen, for example, then number seven would be represented by ///////.
Tally marks represent one such system still in common use. The unary system is only useful for small numbers, although it plays an important role in
theoretical computer science.
Elias gamma coding, which is commonly used in
data compression, expresses arbitrary-sized numbers by using unary to indicate the length of a binary numeral.
The unary notation can be abbreviated by introducing different symbols for certain new values. Very commonly, these values are powers of 10; so for instance, if / stands for one, − for ten and + for 100, then number 304 can be compactly represented as +++ //// and number 123 as + − − /// without any need for zero. This is called a
sign-value notation. The ancient
Egyptian numeral system was of this type, and the
Roman numeral system was a modification of this idea.
More useful still are systems which employ special abbreviations for repetitions of symbols; for example, using the first nine letters of the alphabet for these abbreviations, with A standing for «one occurrence», B «two occurrences», and so on, one could then write C+ D/ for number 304. This system is used when writing
Chinese numerals and other East Asian numerals based on Chinese. The number system of
English language is of this type («three hundred [and] four»), as are those of other spoken
languages, regardless of what written systems they have adopted. However, many languages use mixtures of bases, and other features, for instance 79 in French is
soixante dix-neuf (60 + 10 + 9) and in Welsh is
pedwar ar bymtheg a thrigain (4 + (5 + 10) + (3 × 20)) or (somewhat archaic)
pedwar ugain namyn un (4 × 20 − 1). In English, one could say «four score less one», as in the famous
Gettysburg Address representing «87 years ago» as «four score and seven years ago».
Task 5. Discuss the topic “Numeric systems” with the partner.
Task 6. Review what you have spoken about in the unit “Numerals”. Make a list of the main points and tell the class what you know about numerals.
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