Converting Binary Numbers and Positional Number Systems

In order to convert the binary number 110010101 to a decimal number a few simple steps need to be taken. The first is to count out the number of digits, in this case there is nine. Now assign the right most digit 2 to the power of 0, then the next 2 to the power of 1 and so on until the last digit which should be 2 to the power of 8. Next find the values of each power. After you do this add together all the values that represent a one in the binary number. Your decimal number should be 405.

Going the other way is just as easy. Starting with the number 529 divide by 2. If there is a remainder record it with a 1 if not a 0. Next take the quotient of 529/2 and divide that by 2 record either a 1 or zero in the same manner on the left side of the prevoious digit. Continue doing this until the quotient is zero. Your binary number should be 1000010001.

The differnce between a positional and non positional number system is that in a positional number system the value of each digit is determined by its position. Whereas in a non positional number system the position does not change the value. For example the number 981 and 198 are different numbers in a positional number system but would be the same number in a non positional number system. So with this both binary and decimal number systems are positional number systems.