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With the first number being 1 (not zero), the 25th number is 11001 (base 2). This is 16 + 8 + 1 = 25 (in base ten). Each place value in the binary system is double the value to the right of it.
It is a number system that uses the digits 0 and 1 only. So 0 is written 0 and 1 is 1, but two in base 10 is written 10 in binary. The first digit is 20 or 1, the next is 21 or 2, the next digits is 22 This keeps going and any number can be written in binary or base two.
the Mayan and Chinese are the oldest.
Almost exactly like the decimal system, but the base is the number 2, instead of the number 10. This refers to the place-value system: in decimal, each digit has a place-value that is 10 times as much as the digit on the right; in binary, the factor is 2. It is helpful if you understand the place-value system in decimal first.
The term binary means based on two numbers only. It would be possible to use any two numbers for a binary system, however, since 0 and 1 are the first two numerals, it was considered reasonable to use those. It could just as easily have been 1 and 2. The advantage of a binary system is that it is easily converted to an electrical circuit state; one number means on, the other number means off. That makes it useful for computers, which are based on electrical circuits.