The binary system is the most widespread in information technologies, the industries of communication. Computers understand only the binary code in which current sends two signals - logical "zero" (there is no current) and "unit" (there is current). Understanding of the program code and a difficult technique requires understanding of Boolean algebra - operations in a binary system.
Instruction
1. The easiest way of performance of arithmetic operations is to transfer binary numbers to a habitual decimal system, to make actions in it then to transform result back to binary number. This method is the most clear, but demands accuracy and extra time - instead of one action it is necessary to execute whole four.
2. For the translation of number from a binary system in decimal it is necessary to use the rule of degrees and categories. Each figure of binary number is multiplied by the two in category degree, beginning from zero. After that all intermediate works are put and receive result in a decimal system. So 100 in a binary system it is possible to present in the form of the sum of two zero and unit increased by the two in the second degree. In decimal degree number 4 will turn out.
3. For back translation it is necessary to divide in a column decimal number into the two from the rest, repeating process of division private until it turns out in it (private) "0" or "1". All remains need to be written down. At the end you overturn record of the remains on the contrary and you receive result in a binary system.
4. If you want to make calculations directly in a binary system, you need to study arithmetic tables: additions, multiplication and division. They can strongly surprise the person who was earlier not facing the position numeral systems other than decimal. It is desirable to make actions in a column - so easier to avoid annoying mistakes.
5. Rules for addition are simple: 0 + 0 = 0; 0 + 1 = 1; 1 + 1 = 10. The last sum designates transition of the two to the new category. Use these simple rules for addition of binary numbers in a column. Like addition also examples on subtraction are solved: 0 - 0 = 0; 1 - 0 = 1; 10 - 1 = 1.
6. The table for multiplication corresponds to the decimal analog. The truth of numbers is less here: 0 * 0 = 0; 1 * 0 = 0; 1 * 1 = 1. Division is made in a column by subtraction to similarly decimal system.