Execution of the laboratory work

1. Find your task in Table 4.1 (the last figure of your student’s card is the number of your variant).

2. Make up a flowchart of finding the most probable value and the root-mean-square error of the measured values and calculating the absolute and relative measurement errors for the given value of confidence probability: 0.9, 0.95, and 0.99, taking account of the accuracy class of the measuring device.

3. Write a program in a high-level language, input it into your computer, and run it.

Contents of the Experimentation Paper

1. Working formulas.

2. Computational algorithm in the form of a flowchart.

3. Program execution results.

4. Conclusions (analysis of the obtained results).

Questions for the Self-Testing

1. What are absolute and relative measurement errors?

2. What does the Gaussian distribution of a random value look like?

3. What is the estimate of mathematical expectation and how is it calculated?

4. What is the variance of random value distribution and what is its physical meaning?

Exercises and tasks

1. What is the structure of numerical data representation in DL coding?

2. Convert the following binary data into DL representation.

- 101010101010.0, 000010101010.0, 10001010000001.0;

- 10101.0101010, 000110111.111, 00000101.00001;

- 0.1110101010, 0.000000001111, 0.010101010000001.

3. Calculate the number ranges of the DL data for the following word length: n = 4, 8, 16, and 24.

4. Calculate the increasing factors of the number ranges for the DL representations vs. binary representations with the following word length: n = 4, 8, 16, and 24.

5. What is the binary word length necessary for the significant digits DL representations of the following numbers: 16662373489, 4748, 27, 0, 0.273883939, 0.0000000100001?

6. Convert the following DL represented numbers into binary ones:

- 0,8,10.8.4.2.0.-1.-3.-5.;

- 1,10,11.9.7.6.5.3.2.0.-2.-5.;

- 0,6,123.4.2.0.-1.-56.

7. Determine the binary word length of the following DL numerical data being converted into binary representations:

-0,8,202.189.111.34.12.5.-40.-102.;

- 1,3,2000.0.-333.;

- 0,7,7.6.5.4.3.2.-227.

8. What is the result of the exponent calculation using DL representation of x¹²⁹, if x₁₀ = 16?

9. Compute the fourth power of the number 0,4,6.3.1.-1.

10. Compute the third root of the number 0,3,18.7.2.

11. Compute simultaneously the sum of the following DL numbers:

0,5,8.4.2.0.-10.;

0,12,34.22.21.10.7.4.3.2.0.-2.-4.-5.;

0,7,10.9.3.1.0.-3.-4.;

0,9,13.12.10.7.5.4.-1.-2.-5.

List of literature

1. Gamayun V.P. Application of Digital Logarithmic Data Representation for Realizing Operations of Multiplication, Raising to a Power and Taking the Root. // Engineering Simulation. / V.P. Gamayun. – 1998. – Vol. 15. – P. 641-651.

2. Гамаюн В.П. Применение разрядно-логарифмического представления данных для реализации операций умножения, возведения в степень и извлечение корня // Электронное моделирование. / В.П. Гамаюн. – 1997. – Т. 19, № 5. – С. 70-79.

3. Байков В.Д. Специализированные процессоры: Итерационные алгоритмы и структуры. / В.Д. Байков, В.Б. Смолов. – М.: Радио и связь, 1985. – 288 с.

4. Peterson J.L. Petri Net Theory and the Modeling of Systems. / J.L. Peterson. – Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1981.

5. Питерсон Дж. Теория сетей Петри и моделирование систем / Дж. Питерсон. пер. с англ. – М.: Мир, 1984. – 264 с.

6. Гамаюн В.П. Моделювання багаторозрядних комп’ютерних систем. / В.П. Гамаюн: навч. посібник. – К.: Книжкове вид-во НАУ, 2007. – 112 с.

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