Transcript AVOP-ELEKTRO-HOL-003

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.
Numerical systems
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 units
10 = 101 tens
100 = 102 hundreds
1000 =103 thousands
Writing of a number in a decimal numerical system:
We have number 253
We read : two hundred fifty three.
2 * 100 = 2 * 102
5 * 10 = 5 * 101
3*1
= 3 * 100
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.
321,1 = 3 * 102
2 * 101
2 * 100
1 * 10-1
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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:
1*103 + 2*102 + 3*101 + 3*100 = 123410
1*25 + 1*24 + 0*23 + 0*22 + 1*21 + 1*20 = 5110
Counting in the binary and the decimal system is the same.
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
c) Decimal
b) Hexadecimal
d) Octal
Question for 2 000 Kč
How many numbers are used in binary
system?
a) 1
c) 10
b) 16
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
c) 4
b) 3
d) 5
Question for 5 000 Kč
Number 1000 can be written as:
a) 101
c) 102
b) 103
d) 104
Question for 10 000 Kč
Which numerical system is most
frequently used by numerical
systems?
a) 10
c) 60
b) 2
d) 20
Question for 20 000 Kč
How many symbols are used
in the hexadecimal system?
a) 10
c) 60
b) 16
d) 6
Question for 50 000 Kč
What is the value of the binary
number 10112 in the decimal
system?
a) 11
c) 7
b) 29
d) 45
Question for 100 000 Kč
Where is often used the sexagesimal
system?
a) Lenght
measuring
c) Time measuring
b) Common counting
d) In computers
Question for 200 000 Kč
What is the value of the number 1238 in
the decimal system?
a) 6
c) 18
b) 59
d) 83
Question for 500 000 Kč
How many symbols are used in the octal
system?
a) 6
c) 2
b) 8
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
Sorry your answer is wrong.
End of the game
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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-prokonkurenceschopnost
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