In any system of counting, there are exactly the same number of digits as the base. They go from 0 to one less than the base.
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They are essentially precursors of the ten digits which we use today in everyday arithmetic.
No, it's false. "Base two" is another name for the "binary" number system ... the system running inside any kind of digital hardware, including computers. The corresponding name for the decimal number system is "base ten". The 'base' tells you how many digits the system uses to write numbers. "Base ten" uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 . "Base two" makes all of its numbers with only two digits.
The number of digits in a number system is equal to the base of the system. The decimal system is base 10 and has ten digits. Binary has two bits, which is short for binary digits. Hexadecimal has sixteen digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E & F), and so on.
For example, the decimal system we commonly use uses base ten. This means that each position (place-value) is worth ten times more than the position to the right of it. It also means that ten different digits are needed (0-9).
Because we have ten digits and have learned to count in tens. We use the numbers 0, 1, 2, ..., 9: that is ten different digits.