Learning program: Mechanic – electrician

Name of the program: Numerical systems

II. class

Decimal numerical system

Made by: Mgr. Holman Pavel

Projekt Anglicky v odborných předmětech, CZ.1.07/1.3.09/04.0002

je spolufinancován Evropským sociálním fondem a státním rozpočtem

České republiky.

People are used to use the decimal numerical system to describe numbers.

The basis of a decimal system is the number 10.It means that this system has ten symbols:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Decimal system is a position system. It means that it depends on the position of individual numbers, so called orders.

1 = 100 units10 = 101 tens

100 = 102 hundreds1000 =103 thousands

Writing of a number in a decimal numerical system:

We have number 253

Any number can be written in this form.

Everyone, try to write your chosen number by using the addition of powers with the basis ten.

We read : two hundred fifty three.

2 * 100 = 2 * 102

5 * 10 = 5 * 101

3 * 1 = 3 * 100

321,1 = 3 * 102

2 * 101

2 * 100

1 * 10-1

Any number N in any numerical system can be written in the form of a polynomial

Where Z – the basis of the numerical system (for decimal system is z 10. For binary system z=2, for

octal system z=8. For hexadecimal z=16, for sexadecimal z=60. Any number is chosen as a basis of the system, it determines the whole system), it has to be integer bigger than 1.

N – Designation of the number of orders before the order line, it has to be positive integer K – designation of the number of orders after the order line, it has to be positive integer n+k>0 A – coefficient, number in the corresponding order having values varying from 1 to z-1, number

of numbers is then z Decimal system has ten coefficients expressed by numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) Binary system has two coefficients expressed by numbers (0, 1) Hexadecimal system has sixteen coefficients expressed by symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A,

B, C, D, E, F) Octal system has eight coefficients expressed by numbers (0, 1, 2, 3, 4, 5, 6, 7) Sexadecimal system has sixty coefficients expressed by numbers (0, 1, 2, 3, 4, 5,… …, 56, 57,

58, 59) Any system, for example twentytwo- system, has twenty two coefficients, expressed by

numbers (0, 1, 2, 3, 4, 5,… …, 16, 17, 18, 19, 20, 21)

Number 123410 in the decimal system and 1100112 in binary system tally to these additions of products:

Counting in the binary and the decimal system is the same.

1*103 + 2*102 + 3*101 + 3*100 = 123410

1*25 + 1*24 + 0*23 + 0*22 + 1*21 + 1*20 = 5110

We use the decimal system in common life and while using arithmetical operations we have always unequivocal result. But this system isn’t suitable for computers and numerical systems, because numerical device would have to distinguish ten different states. It would be demanding to its accuracy, quality and performance. That’s why we use systems with the different basis in numerical method. Most frequently used basis is 2 (numbers 0 and 1).

Decimal system – has ten states (z=10), use for mathematic operations in common life, we are used to that and it’s suitable for us. But they are not suitable for numerical method.Binary system – Has two states (z=2), use for technical processing of the information using two numbers 0 and 1. Using these two numbers we can project any numerical value, but the number written in the binary system is very confusing for us compared to the one in the decimal system. It is definitely not suitable for practical use in everyday life, but it is very suitable for the numerical processing of the information in technical practice.Hexadecimal system – has sixteen states (z=16), this system is used in microprocessors and in relation with computers in general. The basis consists of sixteen symbols, mainly numbers, and there are also letters. Compared to clearly binary system the advantage is that 8bit words are projected via simple two-figure numbers. The hexadecimal system is used in modern integrated circuits of coders and decoders, while expressing values in the computer technology for example orientation in addressing the memory. Octal system – has eight states (z=8). It is important mainly as a form of the writing of binary numbers designated for processing or acquired as results of the processing in numerical computers. Sexagesimal system – has sixty states (z=60), use for expressing time.

Question for 1 000 Kč

Which numerical system is most frequently used by people?

a) Binary

b) Hexadecimal

c) Decimal

d) Octal

Question for 2 000 Kč

How many numbers are used in binary system?

a) 1

b) 16

c) 10

d) 2

Question for 3000 Kč

Which number is on the position of tens in the number 12345 in the decimal numerical system?

a) 2

b) 3

c) 4

d) 5

Question for 5 000 Kč

Number 1000 can be written as:

a) 101

b) 103

c) 102

d) 104

Question for 10 000 Kč

Which numerical system is most frequently used by numerical systems?

a) 10

b) 2

c) 60

d) 20

Question for 20 000 Kč

How many symbols are used in the hexadecimal system?

a) 10

b) 16

c) 60

d) 6

Question for 50 000 Kč

What is the value of the binary number 10112 in the decimal system?a) 11

b) 29

c) 7

d) 45

Question for 100 000 Kč

Where is often used the sexagesimal system?

a) Lenght measuring

b) Common counting

c) Time measuring

d) In computers

Question for 200 000 Kč

What is the value of the number 1238

in the decimal system?

a) 6

b) 59

c) 18

d) 83

Question for 500 000 Kč

How many symbols are used in the octal system?

a) 6

b) 8

c) 2

d) 16

Question for 1 000 000 Kč

Determine the value of the number 111010112 in the decimal system.

a) 193 b) 215

c) 235 d) 251

End of the game

Sorry your answer is wrong.

Mužík, J. Management ve vzdělávání dospělých. Praha: EUROLEX BOHEMIA, 2000. ISBN 80-7361-269-7.

Operační program Vzdělávání pro konkurenceschopnost, ESF 2007 – 2013. Dostupné na: http://www.msmt.cz/eu/provadeci-dokument-k-op-vzdelavani-pro-

konkurenceschopnost MALINA, V. Digitální technika. České Budějovice: KOPP, 1996 KRÝDL, M. Číslicová technika. Dubno, 1999 PODLEŠÁK, J., SKALICKÝ, P. Spínací a číslicová technika. Praha, 1994 PECINA, J. Ing. PaedDr. CSc.; PECINA, P. Mgr. Ph.d. Základy císlicové techniky. Brno,

2007