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/ je spolufinancován Evropským sociálním fondem a státním rozpočtem České republiky.

Numerical 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. DBOH DBOH A B C D E F

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 (8) = 1* * * * (8) = (8) = 684 (10) 684 : 16 = 42 remainder : 16 = 2 remainder 10 2 : 16 = 0 remainder (8) = 2AC (16)

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 (2) to the octal system. 101 (2) = 5 (8) 011 (2) = 3 (8) 111 (2) = 7 (8) (2) (2) = 537 (8)

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 we will get the wrong result. 234 (8) = (2) Conversion of numbers from the binary numerical system to the octal. Exercise no. 4: Convert the number 234 (8) to the binary system (8) 2 (8) = 0103 (8) = (8) = 100 Exercise no. 3: Convert the number 57 (8) to the binary system. 5 (8) = 1017 (8) = (8) = (2)

Conversion from the binary to the octal system: Conversion from the octal to the binary system: (2) = (2) = (2) = (2) = (2) = Solution: (2) (2) (2) (2) (2) 64 (8) = 72 (8) = 100 (8) = 172 (8) = 255 (8) = Solution: 255 (8) 271 (8) 217 (8) 341 (8) 203 (8)

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

Question for Kč What is the value of the number 23 (8) in the binary system? a) b) c) d) 10101

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

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

Question for Kč What is the value of the number 131 (8) in the binary system? a) b) c) d)

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

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

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

Question for Kč What is the value of the number 123 (8) in the binary system? a) b) c) d)

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

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

End of the game Sorry your answer is wrong.

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