Except a habitual decimal numeral system in mathematics there is a set of other ways of representation of numbers, including in a binary look. Only two symbols, 0 and 1 are for this purpose used that does a binary system convenient when using in operation of various digital devices.

## Instruction

1. Numeral systems in mathematics are intended for symbolical display of numbers. In usual life, the decimal system which is very convenient for calculations, including in mind is generally used. In the world of digital devices, including computer which became for many the second house now the binary system has the greatest distribution, further in process of decrease of popularity go octal and hexadecimal.

2. These four systems have one general quality – they are position. It means that the value of each sign in total number depends on in what position it costs. From here the concept of word length follows, in a binary look unit of word length is number 2, in decimal – 10, etc.

3. There are algorithms of the translation of numbers from one system in another. These methods are simple and do not demand big knowledge, however development of these skills requires some skill which is reached by practice.

4. A transfer of number from other numeral system in binary is made in two possible ways: or by means of record of each separate sign of number in the form of the four of binary symbols which are table values however can be found iterative division on 2 and independently in view of the simplicity.

5. Use the first method for reduction in a binary type of decimal number. It especially is convenient that it is easier to operate with decimal numbers in mind.

6. For example, transfer number 39 to binary you vidrazdelit 39 on 2 - it will turn out 19 and 1 in the rest. Make some more iterations of division on 2 until finally the rest is equal to zero, and meanwhile write down the intermediate remains at line from right to left. Final enrollment of units and zero will also be your number in a binary look: 39/2 = 19 → 1;19/2 = 9 → 1;9/2 = 4 → 1;4/2 = 2 → 0;2/2 = 1 → 0;1/2 = 0 → 1. So, binary number 111001 turned out.

7. To transfer to a binary look number from numeral systems on the bases 16 and 8, find or make tables of the corresponding designations of each digital and symbolical element of these systems. Namely: 0 0000, 1 0001, 2 0010, 3 0011, 4 0100, 5 0101, 6 0110, 7 0111, 8 1000, 9 1001, A 1010, B 1011, C 1100, D 1101, E 1110, F 1111.

8. Write down each sign of initial number according to data of this table. Examples: Octal number 37 = [3 = 0011; 7 = 0111] = 00110111 in a binary look; Hexadecimal number 5FEB12 = [5 = 0101; F = 1111; E = 1110; B = 1011; 1 = 0001; 2 = 0010] = 010111111110101100010010 in a binary system.