Every 1 or 0 means either yes or no, or on or off; and every binary number 1 represents 2 to the power of its place. So, for the number 110010101, you start with the unit on the far right. That number, 1, represents 2^0, the second number is a 0, which represents 2^1, but since it is a zero, we do not count that number. the third number from the left is 1, and represnts 2^2, which is 4. You will want to repeat this process until you get all the numbers, and add up all the "ones." This would end up being, 1+4+16+128+256 which is equal to 405.
To convert the number 529 into a binary number you do the following. Take the number given, and divide by 2, if that number does not have a remainder the number is 0, and if it does have a remainder, then the binary number is 1. 529 divided by 2 is 254.5, so this is going to be a "1" in the "ones place." After that you round down the number you got before, which was 254.5, rounded down to 254, and divide that number by 2 and get 127. This number does not have a remainder so you are going to want to put a "0" in the "tens place." repeat this process of rounding down when the number has a remainder and putting "0's" when there is a remainder, and "1's" when there is a remainder. The binary number would then be 1000010001.
A positional numbering system is when each position is related to the next by a constant multiplier.
A non-positional numbering system uses symbols or punctuations but do not necessarily need a spot for "0." "144 might be I.IV.IV. in decimal notation" (Wikipedia).