This is called positional because a digit's "place" in the sequence determines its weight. The least significant digit, in the rightmost position, has a weight of 1. The next digit to the left has a weight of 10. The most significant digit, in the leftmost position, has a weight of 100.
Each additional position to the left has a weight 10 times as much as the position to its immediate right. This is why the decimal number system is called a base 10 system. You should also notice that numbers are represented by sequences consisting of the ten digits 0 through 9.
The binary number 100110102 denotes the same quantity as the decimal number 15410. We can always place a binary number into base 10 by expanding it using positional notation.
Octal and Hexadecimal Numbers Writing down even relatively small quantities in base 2 requires a large number of bits. To simplify the chore, designers have introduced alternative octal and hexadecimal number systems, based on 8 and 16 digits, respectively. It is easy to convert between binary and these systems, because the base in each case is a power of 2.
An octal number is represented by a sequence of digits drawn from 0 through 7. For example, the number 2328 denotes the same quantity as 15410. We can verify this by expanding the positional notation:
Converting from base 16 is very similar. Remember that the 16 digits used in the hexadecimal system are 0 through 9 and A through F. Thus, the hexadecimal number 9A16 can be expanded as follows:
Once again, the hexadecimal represents the same quantity as 15410.
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