Binary numeral system - a position numeral system with the basis 2. All numbers in it to a system register by means of two symbols - 0 and 1. The binary numeral system has rich history and is still used in computer facilities. It gave an impetus in development of cybernetics.
Instruction
1. At addition of numbers in a binary system it is important to remember that it has only two symbols - 0 and 1. No other symbols can be in it. Therefore addition of two units 1+1 gives not 2, as in a decimal system, and 10 as is 10 the number following unit in a binary system. It is necessary to remember the simplest rules of addition in a binary system: 0+0 = 0, 1+0 = 0+1 = 1, 1+1 = 10. These rules are necessary to put numbers in a binary system in a column. Apparently, in case of addition of unit to unit, unit goes to the following category. It is obvious that addition of zero to any binary number will not change this number.
2. It is convenient to put large binary numbers in a column. Rules in a binary system are similar to addition to rules of addition in a column in a decimal system. Let there are numbers 1111 and 101. We write down number with the smaller number of categories 101 under number 1111 - the figure of the category of one number has to be located over figure of the same category of other number. Now it is possible to put these numbers. In the first category 1+1 gives 10 - you write down 0 under units in the first category. Unit from 10 passes into the sum of figures of the second category. In the second category 1+0. After addition of unit from the first category 10 will turn out too. Unit passes already into the third category, and in the second category of the sum there will be zero too. In the third category 1+1+1 (unit passed here!) gives 11. In the third category of the sum will be 1, and other unit from number 11 will pass into the fourth category. The fourth category has only number 1111. 1+1 = 10. Thus, 1111+101 = 10100.
3. The reviewed example can be written down in a column of 1111 + 101-----10100