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.

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.

D B O H

0 0 0 0

1 1 1 1

2 10 2 2

3 11 3 3

4 100 4 4

5 101 5 5

6 110 6 6

7 111 7 7

8 1000 10 8

D B O H

9 1001 11 9

10 1010 12 A

11 1011 13 B

12 1100 14 C

13 1101 15 D

14 1110 16 E

15 1111 17 F

16 10000 20 10

17 10001 21 11

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* 62 + 5*61 + 4*60

254(6) = 72 + 30 + 4

254(6) = 106(10)

106 : 2 = 53 remainder 0

53 : 2 = 26 remainder 126 : 2 = 13 remainder 013 : 2 = 6 remainder 16 : 2 = 3 remainder 03 : 2 = 1 remainder 11 : 2 = 0 remainder 1

254(6) = 1101010(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 1010111010001111(2) to the hexadecimal system.

1010(2) = A

1110(2) = E

1000(2) = 8

1111(2) = F

1010 1110 1000 1111(2)

1010111010001111(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 216 just by the number 102 instead of 00102 we will get the wrong result.

A(16) = 1010

A3B8(16) = 1010001110111000(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) = 0011 B(16) = 1011 8(16) = 1000

Exercise no. 3: Convert the number E7(16) to the binary system.

E(16) = 1110 7(16) = 1111

E7(16) = 11101111(2)

Conversion from the binary to the hexadecimal system:

Conversion from the hexadecimal to the binary system:

10101101(2) =

10111001(2) =

10001111(2) =

11100001(2) =

10000011(2) =

Solution:10101101(2)

10110001(2)

101100(2)

1010111(2)

10111010(2)

AE(16) =B2(16) =2C(16) =57(16) =BA(16) =

Solution:AD(16)

B9(16)

8F(16)

E1(16)

83(16)

Question chart:

1

222

3

for 100 for 500 for 300

A B C D

E F G H

Prémie Prémie

Prémie33

1 1

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 10101(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

Question for

300

What is the value of the binary number 11111111(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

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