Binary and Decimals

To convert 110010101 to decimal I first have to separate each position and define them by the base of 2:

1 1 0 0 1 0 1 0 1
2^8 2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0

Then, where ever there is a one, I use the 2^n below it, and add them all together:

256 + 128 + 0 + 0 + 16 + 0 + 4 + 0 + 1 = 405

110010101 = 405

Next, I must convert 529 into Binary. So Im going to map it out like before, just using the powers of 2, starting arbitrarily from 2^9, just to go another step just in case:

2^9 2^8 2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
512 256 128 64 32 16 8 4 2 1

Now, using these numbers, 529 can be made from adding 512+16+1, so the Binary representation will be 1000010001

529 = 1000010001

The difference between positional and non-positional number systems is the following:

A Positional Number System is one where the position of a number is related to the next by a constant multiplier. For example, in decimal the multiplier, or base, is ten. That is to say, the first position is represented by 10^0, the next 10^1, etc etc.

A Non-Positional Number system is one where the number of symbols represent the number. For example, say the smbol is *, in a Non-Positional Number System, * = 1, **=2, ***=3, and so on.