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"Support of teaching technical subjects in English “

"Support of teaching technical subjects in English “. Learning program: Mechanic – electrician Name of the program: Numerical systems II. class Conversions between systems Made by: Mgr. Holman Pavel. Projekt Anglicky v odborných předmětech, CZ.1.07/1.3.09/04.0002

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"Support of teaching technical subjects in English “

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  1. "Support ofteachingtechnicalsubjects in English“ Learning program: Mechanic – electrician Name of the program: Numerical systems II. class Conversions between systems 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.

  2. Numerical systems

  3. Conversions between systems In the numerical method we most often use numbers in the binary system. But numbers in the binary system are too long and poorly arranged. Octal and hexadecimal systems are often used in the numerical method as the more transparent and shorter alternative for the numerical record in the binary system.

  4. Převody mezi soustavami If we want to convert numbers between arbitrary numerical systems, there is a universal way how to do it. First of all we convert the chosen number to the decimal system and than we convert it into the chosen system. Exercise no. 1: Convert the number 254(6) to the binary numerical system. 106: 2 = 53 remainder 0 254(6) = 2* 62 + 5*61 + 4*60 53 : 2 = 26 remainder 1 254(6) = 72 + 30 + 4 26 : 2 = 13 remainder 0 254(6) = 106(10) 13 : 2 = 6 remainder 1 6 : 2 = 3 remainder 0 3 : 2 = 1 remainder 1 1 : 2 = 0 remainder 1 254(6) = 1101010(10) Disadvantages of this method are its complicatedness and time demands.

  5. Conversions between systems Conversion of numbers from the binary system to the hexadecimal system. As you can see in the previous chart, the four-bit number in the binary system (in other words up to four digit number) can be elegantly recorded in the octal system by using only one digit number. Exercise no. 2: Convert the number 1010111010001111(2) to the hexadecimal system. Instruction: Start on the right side and divide the binary number into fours. Using the chart you can easily express it in the hexadecimal system. 1010 1110 1000 1111(2) 1110(2) = E 1111(2) = F 1010(2) = A 1000(2) = 8 1010111010001111(2) = AE8F(16)

  6. Conversions between systems Conversion of numbers from the binary numerical system to the hexadecimal. . The same method can be used in the case of backwards conversion. Don‘t forget that each symbol in the hexadecimal system (it doesn‘t apply for the one in the highest order) must be substituted by four symbols in the binary system. For example if we substitute the number 216just by the number 102 instead of 00102we will get the wrong result. Exercise no. 3: Convert the number E7(16) to the binary system. E(16) = 1110 7(16) = 1111 E7(16) = 11101111(2) Exercise no. 4: Convert the number A3B8 (16) to the binary system. A 3 B 8(16) 3(16) = 0011 B(16) = 1011 8(16) = 1000 A(16) = 1010 A3B8(16) = 1010001110111000(2)

  7. Exercises Conversion from the binary to the hexadecimal system: 10101101(2) = Solution: AD(16) B9(16) 8F(16) E1(16) 83(16) 10111001(2) = 10001111(2) = 11100001(2) = 10000011(2) = Conversion from the hexadecimal to the binary system: Solution: 10101101(2) 10110001(2) 101100(2) 1010111(2) 10111010(2) AE(16) = B2(16) = 2C(16) = 57(16) = BA(16) =

  8. Activity for pupils - Game The End Question chart: for 100 for 300 for 500 1 1 1 Prémie Prémie 2 2 2 3 3 3 Prémie A B C D E F G H

  9. Activity for pupils - Game Question for 100 What is the value of the binary number 101(2) in the decimal system?

  10. Activity for pupils - Game Question for 100 What is the value of the binary number 10101(2) in the decimal system?

  11. Activity for pupils - Game Question for 100 What is the value of the hexadecimal number A1(16) in the decimal system?

  12. Activity for pupils - Game Question for 300 What is the value of the binary number 1010(2) in the hexadecimal system?

  13. Activity for pupils - Game Question for 300 What is the value of the binary number 1101(2) in the hexadecimal system?

  14. Question for 300 What is the value of the binary number 11111111(2) in the hexadecimal system?

  15. Activity for pupils - Game Question for 500 What is the value of the hexadecimal number AB(16) in the binary system?

  16. Activity for pupils - Game Question for 500 What is the value of the hexadecimal number B8(16) in the binary system?

  17. Activity for pupils - Game Question for 500 What is the value of the hexadecimal number 123(16) in the binary system?

  18. Literature • 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

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