Introduction. Computers, algorithms

Transcription

1 Introduction Computers, algorithms

2 Computer mathematical engine that processes programs and data it uses some physical principle, for example: mechanical computers Pascal electronic computers after the 2nd World War computer processes: programs system programs and apliccations data originally only numbers mathematical problems numerical solving of differential equations texts, pictures, sound,

3 Computer computer transforms input data to input data input data Computer output data are represented in digital computers by binary digits 0,1

4 architecture of todays computers was designed in 1947 by American mathematician of Hungarian origin John von Neumann Basic attributes of the architecture: 1. Architecture is independent of the processed task, the behavior of the computer is controlled by the programm, that is stored in the memory (program is sequence (flow) of instructions). 2. Memory is common for program and data. 3. Memory is divided into cells with linear organization; cell is identified by its address (address reference number)

5 4. Instructions, addresses, data, control signals are represented by binary signals (binary system) 5. Instructions are processed in the sequential order, how they are stored in the memory; the order can be change with the special instruction JUMP. 6. No operand (processed data) is usually stored in the instruction, but reference (address) to the data consequence: the program is universal, it works not only with constants stored in instruction but with data stored in memory (and read from keyboard, disk, )

6 Software equipment of PC BIOS (Basic Input Output System) stored in Flash EEPROM basic routines (programs) to control hardware (input and output operations), for example: reading/writing block of data from/to harddisk control videocard operating system (OS) basic software(administrator of sources memory, disk) it provides an environment for users to control computer (GUI - graphical user interface)and for application program to run

7 OS makes access to SW and HW resources access to files on disk, access to networks application software text editors,

8 Programming once more the behavior of digital computer is controlled by the program program is a sequence of elementar command (instructions) coded binary, it is stored in memory program (instructions) is executed by processor the set of instructions of some processor is called instruction set; the set and binary coding of instructions are determined by the designer of processor

9 Instruction consist of: 1. command binary coded operation (add, multiply, mov data, ) 2. operand/operands data to operate direct constant is stored directly in instruction indirect - adresa of memory cell, where operand is stored

10 Examples of instructions arithmetic add two numbers stored in registers, multiply two numbers compare two numbers in registers jumps unconditional jump to address x (i.e next executed instruction is at address x) conditional jump to address x, if result of previous operation is equal to 0

11 moving data move data from memory cell of address x to the internal register inside processor there are special memory cell called registers to store result or intermediate results due to fast access: operations are processed between registred inside processor přesuň data from internal register to the peripheral device

12 program is a sequence of binary numbers (= coded instructions) such program is written in machine code in the era of beginning (50th) programmers wrote programs directly in machine code: first level of the programming superprogramers knew binary codes of instructions from their memory and they were able to write programs in binary digits without list of instruction it is said Mr. S. Cray (designer of the first parallel computer) be able to dictate machinery code of his operation system kernel using telephone

13 such way of programming is slowly and blind and second level of the programming: assembler text mnemonic code of instruction (abreviations) ADD addition, CMP - compare, JZ - jump zero conditional jump jump to address, if result of previous operation is zero program = text in assembler

14 program in assembler is an input of another program called. compiler, which transform assembler into machine code (runable program) example of assembler: ADD AX, BX // add to the register AX value in BX CMP AX,5 // compare value in AX with number 5 JZ 1234 // jump to address 1234, if result of CMP is zero (comparison in computer is realized by subtraction, i.e. result of previous operation is zero, if value in AX is 5

15 advantage of assembler: programs are created easily disadvantage of assembler programmers must know architecture and instructions of given processor; program is not portable to other platform notation of the program is far from mathematic and natural language assembler is a low level language

16 third level: from 60th: high level programming languages (Fortran, Cobol, Pascal, Basic, C, Java, Javascript) text of program written in some high level programming language is similar to the natural language (structured English) and to the mathematical notation program is compiled to the machinery code (runnable program) using compiler program written in high level programming language is readable, understandable, portable to compile the code under others OS, for another platform (processor) small changes are sufficient, we use only another compiler

17 Algorithms

18 Algorithms algorithm technique, how to solve some problem written in formal (structured) way it is a sequence of some elemental steps (instructions, commands) you know basic algorithm: process how to compute roots of quadratic equation cookery book: recipe an object who executes algorithm is a processor processor determines elementar steps

19 example: recipe how to prepare cake cook(man) is a processor, elemental steps are: take 2 eggs, algorithm to compute roots of quadratic equation for computer processor is a computer processor, elemental steps are binary coded instruction of given processor to write a program means: think out algorithm (how to solve a problem) and write down algorithm in some high level programming language

20 Example: Algorithm to solve quadratic equation 1. if a=0 go to the step 8 2. D = b 2-4ac 3. if D < 0 go to the step 6 4. Equation has two real roots 5. End 6. Equation has two comlex roots 7. End 8. etc.

21 Features of algorithms elemental consist of finite numbers of elemental steps deterministic it is possible to determine after the execution of each step if the process finishes (i.e. which is the next step to be executed) finite total count of the steps is finite massed (universal) it is useful to solve set of similar tasks

22 Basic components of the algorithms: 3 components: 1. simple sequence of commands 2. branching (conditions) selection of the next step (instruction) depends if a condition is satisfied or not 3. cycles (loops) steps are executed repeatedly loops with given count of repeating loops with condition (at the end of the loop/at the beginnig of the loop)

23 Algorithm notation flowcharts (graphical notation) steps of the algorithm are expressed by special graphical symbols depending on the type of the operation the sequence of steps execution is determined by arrows the flowchart is oriented graph

24 START / END of the algorithm action (command) START s = a * b condition (branching) a < b yes, +, 1 no, -, 0

25 There exist special symbols for cycles, input/output operations (printing, reading from keyboard), work with files input/output operation Print: The circumference of the circle is r

26 cycle (loop) with given count of repeating called for loop in programming languages i = 1 to 10 Print: 3*i loop body NEXT i

27 loop with condition at the beginning while loop in programming languages are data ready? no wait 1s yes

28 Example: algorithm to compute circumference of the circle START Print: Enter circumreference Read: r 0 r < 0 1 Print: Error, Radius is negative o = 2 * 3.14 * r Print: Circumference is o END

29 structured natural language 1. Print: Enter radius 2. Read: r 3. if r < 0, go to the step 7 4. o = 2*3,14*r 5. Print: Circumference is o 6. End 7. Print: Error: Radius is negative 8. End

30 pseudo-language we use constructs of some programming language but commands are written by free style example: pseudo-language based on Pascal Print: Enter radius Read: r if r < 0 then Print: Error: Radius is negative else begin o = 2*3,14*r Print: Circumference is o end

31 Program written in C programming language printf("enter circumference: "); scanf("%f",&r); if (r<0) printf( Error: Radius is negative"); else { o = 2*3.14*r; printf( Circumference = %f",o); }

32 Tasks Write an algorithm how to prepare a cup of tea Write an algorithm to compute a root of the linear equation ax + b = c Write complete algorithm to compute roots of the quadratic equation ax 2 + bx + c = 0