Guide
1
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 discharge of a figure 2. Thus, in the recording of binary numbers invol
ved only two 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.
7
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.