Learning program: Mechanic – electrician Name of the program: Numerical systems II. class Conversions between systems Made by: Mgr. Holman Pavel Projekt.

Prezentace na téma: "Learning program: Mechanic – electrician Name of the program: Numerical systems II. class Conversions between systems Made by: Mgr. Holman Pavel Projekt."— Transkript prezentace:

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2 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.

3 Numerical systems

4 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. DBOH 0000 1111 21022 31133 410044 510155 611066 711177 81000108 DBOH 91001119 10101012A 11101113B 12110014C 13110115D 14111016E 15111117F 16100002010 17100012111

5 If we want to convert numbers between arbitrary numerical systems, there is an 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. Disadvantages of this method are its complicatedness and time demands. Exercise no. 1: Convert the number 1254 (8) to the hexadecimal system. 1254 (8) = 1*8 3 + 2* 8 2 + 5*8 1 + 4*8 0 1254 (8) = 512 + 128 + 40 + 4 1254 (8) = 684 (10) 684 : 16 = 42 remainder 12 42 : 16 = 2 remainder 10 2 : 16 = 0 remainder 2 1254 (8) = 2AC (16)

6 Conversion of numbers from the binary system to the octal system. As you can see in the previous chart, the three-bit number in the binary system (in other words up to three digit number) can be elegantly recorded in the octal system by using only one digit number. Instruction: Start on the right side and divide the binary number to the threes. Using the chart you can easily express it in the octal system. Exercise no. 2: Convert the number 101011111 (2) to the octal system. 101 (2) = 5 (8) 011 (2) = 3 (8) 111 (2) = 7 (8) 101 011 111 (2) 101011111 (2) = 537 (8)

7 The same method can be used in the case of backwards conversion. Don‘t forget that each symbol in the octal system (it doesn‘t apply for the one in the highest order) must be substituted by three symbols in the binary system. For example if we substitute the number 2 (8) just by the number 10 (2) instead of 010 2 we will get the wrong result. 234 (8) = 10011100 (2) Conversion of numbers from the binary numerical system to the octal. Exercise no. 4: Convert the number 234 (8) to the binary system. 2 3 4 (8) 2 (8) = 0103 (8) = 011 4 (8) = 100 Exercise no. 3: Convert the number 57 (8) to the binary system. 5 (8) = 1017 (8) = 111 57 (8) = 101111 (2)

8 Conversion from the binary to the octal system: Conversion from the octal to the binary system: 10101101 (2) = 10111001 (2) = 10001111 (2) = 11100001 (2) = 10000011 (2) = Solution: 110100 (2) 111010 (2) 1000000 (2) 1111010 (2) 10101101 (2) 64 (8) = 72 (8) = 100 (8) = 172 (8) = 255 (8) = Solution: 255 (8) 271 (8) 217 (8) 341 (8) 203 (8)

9 Question for1 000 Kč What is the value of the number 13 (8) in the decimal system? a)1010 b) 11 c) 12 d) A1

10 Question for 2 000 Kč What is the value of the number 23 (8) in the binary system? a)1011010110 b) 10011 c) 11010 d) 10101

11 Question for 3 000 Kč What is the value of the number 33 (8) in the hexadecimal system? a)2424 b) 1C c) 21 d) 1B

12 Question for 5 000 Kč What is the value of the number 101011 (2) in the decimal system? a)5555 b) 28 c) 43 d) 61

13 Question for 10 000 Kč What is the value of the number 131 (8) in the binary system? a)10110011011001 b) 1110011 c) 1011101 d) 1100111

14 Question for 20 000 Kč What is the value of the number 192 (10) in the hexadecimal system? a)F5F5 b) C0 c) 5B d) 8A

15 Question for 50 000 Kč What is the value of the binary number 1011 (2) in the decimal system? a)1111 b) 29 c) 7 d) 45

16 Question for 100 000 Kč What is the value of the number 172 (8) in the hexadecimal system? a)F6F6 b) C4 c) 5C d) 7A

17 Question for 200 000 Kč What is the value of the number 123 (8) in the binary system? a)11011011101101 b) 1011101 c) 1100111 d) 1010011

18 Question for 500 000 Kč What is the value of the number 255 (8) in the hexadecimal system? a)ABAB b) BC c) CD d) AD

19 Question for 1 000 000 Kč a)273273b) 187 c) 235 d) 215 What is the value of the binary number 10111011 (2) in the octal system?

20 End of the game Sorry your answer is wrong.

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22  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- konkurenceschopnosthttp://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