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Transcript of Learning program: Mechanic – electrician Name of the program: Numerical systems II. class...
Learning program: Mechanic – electrician
Name of the program: Numerical systems II. class
Hexadecimal numerical system
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.
Hexadecimal system– is expressed by the symbol H or by the index (16). Hexadecimal system is a position system and therefore like in other systems each number can be expressed as a sum of products, which consist of numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and letters A, B, C, D, E, F and power of the basis 16, which again determines order or in other words the value.
According to positions in the positional system we can characterize the hexadecimal system this way:
16n; 16n-1;…; 165 = 1048576; 164 = 65536; 163 = 4096; 162 = 256;
161 = 16; 160 = 1; 16-1 = 0,0625; 16-2 = 0,0039; 16-3 = 0,0002; 16-1 = 0,125; …; … ; 16-(n-1); 16-n
Exercise:Express the number1A56(16) in the hexadecimal system according to individual orders and coefficients of the product.
1A5C = 1*163 + 10*162 + 5*161 + 12*160
The value of the number in the hexadecimal system can be easily expressed in the decimal system. You just need to add up individual values of elements in the orderly record of the number.
Exercise: Convert the number 1B3(16) from the hexadecimal system to the decimal numerical system.
1*162 + 11*161 + 3*160 =1*256 + 11*16 + 3*1 = 256 + 176 + 3 = 435
Exercise: Convert the number12CA(16) from the hexadecimal system to the decimal numerical system.
1*163 + 2*162 + 12*161+ 10*160
1*4096 + 2*256 + 12*16 + 10*1 4096 + 512 + 192 + 10 = 4810
Power Variance Result
163 = 4096 6358 – 4096 = 2262 1
162 = 256 2265 – 8*256 = 214 8
161 = 16 214 – 13*16 = 6 D
160 = 1 6 – 6*1 = 0 6
Sequential subtraction method
This method is easily usable for the changeover from one basis to another. The original number is divided by the sequential subtraction of tailing off powers of the new basis, where a desired power of the new basis is smaller or equal to the remaining part of the original number.
Exercise: Convert the number 6358(10) to the hexadecimal numerical system.
Sequential division methodis often considered the basic method of division of the given decimal number by the basis of the hexadecimal system. After the division by the basis 16 we write the result of it by the division to the decimal integers and in the same time we have to determine, what the remainder of the division is. The value of the remainder can be 0 to 15. For values of the remainder 10 to 15 we use lettersA = 10, B = 11, C = 12, D=13, E = 14 a F = 15.In another step we repeat this procedure by division of the previous result by the basis of the system. Again we write down the result of the integer division and the value of the remainder. We repeat this procedure until the result of the division by the system is the number 0. We write down the value of all reminders and record the result. Remainders are written into the result in the reverse order.
Exercise: Express the number 958(10) in the hexadecimal system.
Calculation Partial quotient
Reminder
9548 : 16 = 596 596 12 = C
596 : 16 = 37 37 4
37 : 16 = 2 2 5
2 : 16 = 0 0 2
1005(10) = 254C(16)
Conversion from the hexadecimal to the decimal numerical system
Conversion from the decimal to the hexadecimal numerical system
1B2(16) = A2C3(16) = B1A2(16) = A1B2(16) = ABC(16) =
1BC(16) = A2C(16) = B1A(16) = A1B(16) = BAC(16) =
7B(16) E7(16) FF(16) 64(16) 4D(16)
444(10) 2604(10) 2842(10) 2587(10) 2988(10)
123(10) = 231(10) = 255(10) = 100(10) = 77(10) =
1234(10) = 4321(10) = 1278(10) = 1434(10) = 2012(10) =
4D2(16) 10E1(16) 4FE(16) 59A(16) 7DC(16)
434(10) 41667(10) 45474(10) 41394(10) 2784(10)
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
How many symbols are used in the hexadecimal system?
What is the numerical basis used in the hexadecimal system?
Question for 100
How many letters are used in the hexadecimal system?
Question for 100
What is the value of the hexadecimal number 1A3(16) in decimal system?
Question for 300
What is the value of the hexadecimal number A13(16) in decimal system?
Question for 300
What is the value of the hexadecimal number A2(16) in decimal system?
Question for 300
What is the value of the decimal number 123(10) in the hexadecimal system?
Question for 500
What is the value of the decimal number 248(10) in the hexadecimal system?
Question for 500
What is the value of the decimal number 1234(10) in the hexadecimal 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