Download AVOP-ELEKTRO-HOL-005

Learning program: Mechanic – electrician
Name of the program: Numerical systems
II. class
Octal 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
Octal system – is expressed by the symbol O or index(8). The octal
system is a position system and like in decimal and binary systems
each number can be expressed as an addition of products, which
consist of numbers 0, 1, 2, 3, 4, 5, 6 or 7 or the power of the basis
8, which determine the order or value.
According to positions in a position system the octal system can be
characterized by order this way:
8n; 8n-1;…; 84 = 4096; 83 = 512; 82 = 64; 81 = 8; 80 = 1; 8-1 = 0,125;
8-2 = 0,15625; 8-3 = 0,00195…; 2-4 = 0,000244…; … ; 2-(n-1); 2-n
Exercise:
Express the number 1231,12(2) in octal system according to individual
orders and coefficients of the product.
1231,12(8) = 1*83 + 2*82 + 3*81 + 1*80 +1*8-1 + 2*8-2
The value of the number in the octal system can be easily expressed
in the decimal system. You just have to add individual constituent
values in the order writing of the number.
Exercise: Convert number 1234(8) in the octal system into the
decimal numerical system.
1*83 + 2*82 + 3*81 + 4*80 =
1*512 + 2*64 + 3*8 + 4*1 =
512 + 128 + 24 + 4 = 668
Exercise: Convert number 4321(8) in the octal system into the
decimal numerical system.
4*83 + 3*82 + 2*81 + 1*80 =
4*512 + 3*64 + 2*8 + 1*1 =
2048 + 192 + 16 + 1 = 2257
Sequential subtraction method
This method is easily usable for changeover from one basis to another.
Original number is divided by the sequential subtraction of tailing off
powers of the new basis, where desired power of the new basis is
smaller or equal to the remaining part of the original number.
Exercise:
Convert number 635(10) to the octal numerical system.
Power
Variance
Result
83 = 512
635 – 512 = 123
1
82 = 64
123 – 64 = 59
1
81 = 8
59 – 7*8 = 3
7
80 = 1
3 – 3*1 = 0
3
Sequential division method
For expressing the conversion of the decimal integer the basis of the
conversion is the division of the chosen decimal number by the basis of the
octal system. After the division by the basis 8 we write the result of it by the
division to the decimal integers and in the same time we have to determine,
what the remainder of the division is. The value of the remainder can be 0 to
7.
In another step we repeat this procedure by division of the previous result by
the basis of the system. Again we write down the result rounded on the
decimal integer and the value of the remainder. We repeat this procedure until
the result of the division by the system basis will be the number 0. We will
write down the value of all remainders and record the result. Remainders are
written into the result in the reverse order.
Exercise: Write the number
1005(10) in the octal numerical
system.
1005(10) = 1755(8)
Calculation
Partial
Remin
quotient der
1005 : 8 = 125
125
5
125 : 8 = 15
15
5
15 : 8 = 1
1
7
1:8=0
0
1
Sequential multiplication method
This method is used like in binary and hexadecimal systems most
frequently to express the decimal number smaller than one.
Exercise: Convert the number 0,725(10) to the octal system.
Calculation
Partial result
Result
0,725 x 8 =
5,8
5
0,8 x 8 =
6,4
6
0,4 x 8 =
3,2
3
0,2 x 8 =
1,6
1 etc.
Number 0,725(10) = 0,5631…(8)
The End
Question chart:
Numerical projection
Numerical projection
Numerical projection
for 100
for 300
for 500
Prémie
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Prémie
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1
2
2
2
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Prémie
A
B
C
D
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F
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H
Binary system for100
How many numbers does the octal system use?
Binary system for 100
What is the other name for octal system?
Binary system for 100
What is the numerical basis used in the octal system?
Binary system for 300
What is the value of the octal number 123(8) in the decimal
system?
Binary system for 300
What is the value of the octal number 135(8) in the decimal
system?
Binary system for 300
What is the value of the octal number 213(8) in the decimal
system?
Binary system for 500
What is the value of the decimal number 123(10) in the octal system?
Binary system for 500
What is the value of the decimal number 321(10) in the octal
system?
Binary system for 500
What is the value of the decimal number 1234(10) in the octal
system?
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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