Learning program: Mechanic – electrician Name of the program: Numerical systems II. class Decimal numerical system 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

People are used to use the decimal numerical system to describe numbers. The basis of a decimal system is the number 10. It means that this system has ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Decimal system is a position system. It means that it depends on the position of individual numbers, so called orders. 1 = 10 0 units 10 = 10 1 tens 100 = 10 2 hundreds 1000 =10 3 thousands

Writing of a number in a decimal numerical system: We have number 253 Any number can be written in this form. Everyone, try to write your chosen number by using the addition of powers with the basis ten. We read : two hundred fifty three. 2 * 100 = 2 * * 10 = 5 * * 1 = 3 * ,1 = 3 * * * * 10 -1

 Any number N in any numerical system can be written in the form of a polynomial  Where  Z – the basis of the numerical system (for decimal system is z 10. For binary system z=2, for octal system z=8. For hexadecimal z=16, for sexadecimal z=60. Any number is chosen as a basis of the system, it determines the whole system), it has to be integer bigger than 1.  N – Designation of the number of orders before the order line, it has to be positive integer  K – designation of the number of orders after the order line, it has to be positive integer n+k>0  A – coefficient, number in the corresponding order having values varying from 1 to z-1, number of numbers is then z  Decimal system has ten coefficients expressed by numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)  Binary system has two coefficients expressed by numbers (0, 1)  Hexadecimal system has sixteen coefficients expressed by symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F)  Octal system has eight coefficients expressed by numbers (0, 1, 2, 3, 4, 5, 6, 7)  Sexadecimal system has sixty coefficients expressed by numbers (0, 1, 2, 3, 4, 5,… …, 56, 57, 58, 59)  Any system, for example twentytwo- system, has twenty two coefficients, expressed by numbers (0, 1, 2, 3, 4, 5,… …, 16, 17, 18, 19, 20, 21)

Number in the decimal system and in binary system tally to these additions of products: Counting in the binary and the decimal system is the same. 1* * * *10 0 = * * * * * *2 0 = We use the decimal system in common life and while using arithmetical operations we have always unequivocal result. But this system isn’t suitable for computers and numerical systems, because numerical device would have to distinguish ten different states. It would be demanding to its accuracy, quality and performance. That’s why we use systems with the different basis in numerical method. Most frequently used basis is 2 (numbers 0 and 1).

Decimal system – has ten states (z=10), use for mathematic operations in common life, we are used to that and it’s suitable for us. But they are not suitable for numerical method. Binary system – Has two states (z=2), use for technical processing of the information using two numbers 0 and 1. Using these two numbers we can project any numerical value, but the number written in the binary system is very confusing for us compared to the one in the decimal system. It is definitely not suitable for practical use in everyday life, but it is very suitable for the numerical processing of the information in technical practice. Hexadecimal system – has sixteen states (z=16), this system is used in microprocessors and in relation with computers in general. The basis consists of sixteen symbols, mainly numbers, and there are also letters. Compared to clearly binary system the advantage is that 8bit words are projected via simple two-figure numbers. The hexadecimal system is used in modern integrated circuits of coders and decoders, while expressing values in the computer technology for example orientation in addressing the memory. Octal system – has eight states (z=8). It is important mainly as a form of the writing of binary numbers designated for processing or acquired as results of the processing in numerical computers. Sexagesimal system – has sixty states (z=60), use for expressing time.

Question for Kč Which numerical system is most frequently used by people? a)BinaryBinary b) Hexadecimal c) Decimal d) Octal

Question for Kč How many numbers are used in binary system? a)11 b) 16 c) 10 d) 2

Question for 3000 Kč Which number is on the position of tens in the number in the decimal numerical system? a)22 b) 3 c) 4 d) 5

Question for Kč Number 1000 can be written as: a) b) 10 3 c) 10 2 d) 10 4

Question for Kč Which numerical system is most frequently used by numerical systems? a)1010 b) 2 c) 60 d) 20

Question for Kč How many symbols are used in the hexadecimal system? a)1010 b) 16 c) 60 d) 6

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

Question for Kč Where is often used the sexagesimal system? a)Lenght measuringLenght measuring b) Common counting c) Time measuring d) In computers

Question for Kč What is the value of the number in the decimal system? a)66 b) 59 c) 18 d) 83

Question for Kč How many symbols are used in the octal system? a)66 b) 8 c) 2 d) 16

Question for Kč Determine the value of the number in the decimal system. a)193193b) 215 c) 235 d) 251

End of the game Sorry your answer is wrong.

 Mužík, J. Management ve vzdělávání dospělých. Praha: EUROLEX BOHEMIA, ISBN  Operační program Vzdělávání pro konkurenceschopnost, ESF 2007 –  Dostupné na: konkurenceschopnosthttp://  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