Conversion of Binary Numbers - Decimal Numbers

       Let's see how we take the binary number "10111101" to its equivalent in the decimal number system. To factor must be used on 2, corresponding to the base number and raise to the power that corresponds to each digit, according to its place within the series of numbers. As exponents use the "0", "1", "2", "3"and so on, until the "7", thus completing the total number of exponents that we have to use with the binary number. Factoring the start to do from left to right starting with the highest exponent, as you can see below in the following example:

     In the result we can see that the binary number "10111101" corresponds to the integer 189 in the decimal number system.

     Now, doing the opposite, convert a number belonging to the decimal number system (base 10) to a binary (base 2). First use the same number 189 as a dividend and 2, corresponding to the binary number base number to be found, as a divisor. Then the result or quotient obtained from that division (94 in this case), we divide by 2 again and so we will continue to turn to each ratio to obtain, until it's impossible to continue dividing. Consider the example:

      After the operation, write the numbers of residues of each division in reverse order, that is, making the bottom up. Thus we get the binary number, whose value amounts to 189, which in this case will be "10111101".

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