Guide

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Any system

**notation**- this way of writing numbers with certain characters.There are positional, and mixed systems nonpositional**notation**.Decimal and binary systems are positional, ie,the value of certain figures in the record number is determined depending on what position it occupies. 2

digit position in the number of discharges are called.In the decimal system

**notation**this role*number 10, ie,each digit in the number is a factor of 10 in a corresponding degree.The number of digits starting from zero, and reading takes place from right to left.For example,**number 173 can be read as follows: 3 * 10 ^ 0 + 7 * 10 ^ 1 + 1 * 10 ^ 2.* 3

In the binary system
ved only two

**discharge of a figure 2. Thus, in the recording of binary numbers invol***number*O mark: 0 and 1. For example, the number of*0110 in detailed records looksas follows: 2 * * 0 0 * 1 + 2 * 1 + 1 * 2 ^ 2 + 2 ^ 0 * 3.In the decimal system**it would be equal to the number of*6. 4

Converting from decimal to binary is implemented as integers, and for fractional.Translation of a decimal number produced by successive dividing it by 2. The number of iterations (action) is increased to until the quotient becomes equal to zero, and the resulting number of binary

*written as residues derived from right to left.* 5

For example, the conversion of 19 is as follows: 19/2 = 18/2 + 1 = 9, in the residue - 1, write 1; 9/2 = 8/2 + 1 = 4,in residue - 1, write 1; 4/2 = 2, the residue is absent, write 0, 2/2 = 1, there is no residue, write 0 1/2 + 1 = 0, the residue - 1 write 1.Itak,after application of the method of successive division among the 19 were binary numbers

*10011.* 6

When converting fractional decimal to binary first translated the whole part.Fractional translated into binary code by sequentially multiplying by 2 until the whole until a part which will give one binary number.The figures after the decimal point are written left to right.

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example,

*number*3,4 translated into a binary number*as follows: 3/2 = 2/2 + 1 write 1 ;?= 0 + 1 write 1.Itak, the integer part of 3.4 is 11 in binary system***notation**.Now translate the fractional part of 0.4: 0.4 * 2 = 0.8, write 0; 0.8 * 2 = 1.6, write 1 0.6 * 2 = 1.2, write 1 0.2* 2 = 0.4, write 0; and t.d.Simvolnaya record conversion of two numbers is: 3,4_10 = 11,0110_2.