Converting Binary Numbers

To convert the binary number 110010101 use the following math:

(1 * 2^0) + (0 * 2^1) + (1 * 2^2) + (0 * 2^3) + (1 * 2^4) + (0 * 2^5) + (0 * 2^6) + (1*2^7) +(1 * 2^8) = 405

To convert the decimal number 529 to binary use the following math:

529 mod 2 = 1
529 / 2 = 264.5
264 mod 2 = 0
264 / 2 = 132
132 mod 2 = 0
132 / 2 = 66
66 mod 2 = 0
66 / 2 = 33
33 mod 2 = 1
33 / 2 = 16.5
16 mod 2 = 0
16 / 2 = 8
8 mod 2 = 0
8 / 2 = 4
4 mod 2 = 0
4 / 2 = 2
2 mod 2 = 0
2 / 2 = 1
1 mod 2 = 1
1 / 2 = .5
stop here because.5 rounds down to zero

thus, 529 = 1000010001

A positional number system is a numeral system in which each position is related to the next by a constant multiplier, a common ratio, called the base of that numeral system. A non-positional number system is number system that may be denoted positional systems, but that deviate in one way or another from standard positional systems.