Converting Numbers & the Number System

To convert the # 110010101 to a decimal, I started to utilize the powers of 2 increasing the exponent by 1 each time. For example, I started on the rightmost side with the numeral 1 and made it equal to 2 to the zero, then 0 to the first and so on. Eventually, using these powers I got up to 2 to the 9th. Next I added up all the ones which was 1+4+16+128+256 which equals 405.

The number 529 can be converted into binary by dividing the digit by 2 and thus taking the quotient of that and dividing by 2 until the final remainder is 0. In the dividing process, after getting the quotients you need to take the remainder which can be equal to 0 or 1 and starting from the rightmost side fill in the binary number like so:

529 divided by 2= 264 1
264 " "= 137 0
137 " "= 68 1
68" "= 34 0
34" "= 17 0
17" "= 8 1
8" "= 4 0
4" "= 2 0
2" "= 1 1
1" "= 1/2 0

Thus the answer is 0100100101.


The positional number system is when the value of each digit by its position. In other words "Order Matters". For example, the # 312 is different from the value 213. The non-positional number system is when symbols are utilized to represent numbers like the Roman numeral system is non-positional. For example V would represent the numeral 5.