LECTURE No. 1. Introduction to computer science

1. Computer science. Information. Representation and processing of information

Computer science deals with the formalized representation of objects and the structures of their relationships in various fields of science, technology, and production. To model objects and phenomena, various formal means are used, for example logical formulas, data structures, programming languages, etc.

In computer science, such a fundamental concept as information has different meanings:

1) formal presentation of external forms of information;

2) abstract meaning of information, its internal content, semantics;

3) relation of information to the real world.

But, as a rule, information is understood as its abstract meaning - semantics. By interpreting the presentation of information, we will obtain its meaning, semantics. Therefore, if we want to exchange information, we need consistent representations so that the correctness of interpretation is not compromised. To do this, the interpretation of the presentation of information is identified with certain mathematical structures. In this case, information processing can be performed using strict mathematical methods.

One of the mathematical descriptions of information is its representation in the form of a function y =f(x, t), where t is time, x is a point in a certain field at which the value of y is measured. Depending on the parameters of the chi function (information can be classified.

If the parameters are scalar quantities that take on a continuous series of values, then the information thus obtained is called continuous (or analog). If the parameters are given a certain step of change, then the information is called discrete. Discrete information is considered universal, since for each specific parameter it is possible to obtain the value of a function with a given degree of accuracy.

Discrete information is usually identified with digital information, which is a special case of symbolic information of alphabetical representation. An alphabet is a finite set of symbols of any nature. Very often in computer science a situation arises when the characters of one alphabet must be represented by the characters of another, i.e., a coding operation must be performed. If the number of symbols of the encoding alphabet is less than the number of symbols of the encoding alphabet, then the encoding operation itself is not complex, otherwise it is necessary to use a fixed set of symbols of the encoding alphabet for unambiguous correct encoding.

As practice has shown, the simplest alphabet that allows you to encode other alphabets is binary, consisting of two characters, which are usually designated by 0 and 1. Using n characters of the binary alphabet, you can encode 2n characters, and this is enough to encode any alphabet.

The quantity that can be represented by a symbol of the binary alphabet is called the minimum unit of information or bit. A sequence of 8 bits - a byte. An alphabet containing 256 different 8-bit sequences is called a byte alphabet.

Today, the standard code in computer science is one in which each character is encoded by 1 byte. There are other alphabets.

2. Number systems

A number system is a set of rules for naming and writing numbers. There are positional and non-positional number systems.

A number system is called positional if the value of a digit of a number depends on the location of the digit in the number. Otherwise it is called non-positional. The value of a number is determined by the position of these digits in the number.

3. Representation of numbers in a computer

32-bit processors can handle up to 232-1 RAM, and addresses can be written in the range 00000000 - FFFFFFFF. However, in real mode the processor operates with memory up to 220-1, and addresses fall in the range 00000 - FFFFF. Memory bytes can be combined into fields of either fixed or variable length. A word is a fixed-length field consisting of 2 bytes, a double word is a field of 4 bytes. Field addresses can be even or odd, and operations are performed faster for even addresses.

Fixed-point numbers are represented in a computer as binary integers, and their size can be 1, 2 or 4 bytes.

Binary integers are represented in two's complement, and fixed-point numbers are represented in two's complement. Moreover, if a number occupies 2 bytes, then the structure of the number is written according to the following rule: the most significant digit is allocated to the sign of the number, and the rest - to the binary digits of the number. The complementary code of a positive number is equal to the number itself, and the complementary code of a negative number can be obtained using the following formula: x = 10i - \x\, where n is the digit capacity of the number.

In the binary number system, the additional code is obtained by inverting the digits, that is, replacing ones with zeros and vice versa, and adding one to the least significant digit.

The number of bits of the mantissa determines the precision of the number representation, the number of bits of machine order determines the range of representation of floating point numbers.

4. Formalized concept of an algorithm

An algorithm can only exist if some mathematical object exists at the same time. The formalized concept of an algorithm is associated with the concept of recursive functions, normal Markov algorithms, and Turing machines.

In mathematics, a function is called single-valued if for any set of arguments there is a law by which a unique value of the function is determined. An algorithm can act as such a law; in this case the function is called computable.

Recursive functions are a subclass of computable functions, and the algorithms that define the calculations are called the companion algorithms of recursive functions. First, the basic recursive functions are fixed, for which the accompanying algorithm is trivial and unambiguous; then three rules are introduced - substitution, recursion and minimization operators, with the help of which more complex recursive functions are obtained based on basic functions.

The basic functions and their accompanying algorithms can be:

1) a function of n independent variables, identically equal to zero. Then, if the sign of the function is φn, then, regardless of the number of arguments, the value of the function should be set equal to zero;

2) an identical function of n independent variables of the form ψni. Then, if the sign of the function is ψni, then the value of the function should be taken the value of the i-th argument, counting from left to right;

3) Λ is a function of one independent argument. Then, if the sign of the function is λ, then the value of the function should be taken to be the value following the value of the argument. Various scientists have proposed their approaches to formalized

presentation of the algorithm. For example, the American scientist Church suggested that the class of computable functions is exhausted by recursive functions and, as a consequence, whatever the algorithm is that processes one set of non-negative integers into another, there is an algorithm that accompanies the recursive function and is equivalent to this one. Consequently, if a recursive function cannot be constructed to solve a certain problem, then there is no algorithm for solving it. Another scientist, Turing, developed a virtual computer that processed an input sequence of symbols into an output. In this regard, he put forward the thesis that any computable function is Turing computable.

Author: Tsvetkova A.V.

>> Forward: Pascal language (Introduction to Pascal. Standard procedures and functions. Pascal operators)

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