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 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. Disadvantages of this method are its complicatedness and time demands. Exercise no. 1: Convert the number 254 (6) to the binary numerical system. 254 (6) = 2* * * (6) = (6) = 106 (10) 106 : 2 = 53 remainder 0 53 : 2 = 26 remainder 1 26 : 2 = 13 remainder 0 13 : 2 = 6 remainder 1 6 : 2 = 3 remainder 0 3 : 2 = 1 remainder 1 1 : 2 = 0 remainder (6) = (10)

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. 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. Exercise no. 2: Convert the number (2) to the hexadecimal system (2) = A 1110 (2) = E 1000 (2) = (2) = F (2) (2) = AE8F (16)

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 2 16 just by the number 10 2 instead of we will get the wrong result. A (16) = 1010 A3B8 (16) = (2) Conversion of numbers from the binary numerical system to the hexadecimal.. Exercise no. 4: Convert the number A3B8 (16) to the binary system. A 3 B 8 (16) 3 (16) = 0011B (16) = (16) = 1000 Exercise no. 3: Convert the number E7 (16) to the binary system. E (16) = (16) = 1111 E7 (16) = (2)

Conversion from the binary to the hexadecimal system: Conversion from the hexadecimal to the binary system: (2) = (2) = (2) = (2) = (2) = Solution: (2) (2) (2) (2) (2) AE (16) = B2 (16) = 2C (16) = 57 (16) = BA (16) = Solution: AD (16) B9 (16) 8F (16) E1 (16) 83 (16)

Question chart: for 100for 500for 300 ABCD EFGH Prémie The End

Question for 100 What is the value of the binary number 101 (2) in the decimal system?

Question for 100 What is the value of the binary number (2) in the decimal system?

Question for 100 What is the value of the hexadecimal number A1 (16) in the decimal system?

Question for 300 What is the value of the binary number 1010 (2) in the hexadecimal system?

What is the value of the binary number 1101 (2) in the hexadecimal system? Question for 300

What is the value of the binary number (2) in the hexadecimal system?

What is the value of the hexadecimal number AB (16) in the binary system? Question for 500

What is the value of the hexadecimal number B8 (16) in the binary system? Question for 500

What is the value of the hexadecimal number 123 (16) in the binary system? Question for 500

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