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 Question from SUDHIR, a teacher: What does a number subscripted to another one denote?  (I know that a number superscripted to another denotes the power, but the subscript number is something I have never seen before.)

Hi Sudhir.

One number subscripted to another number generally means a different base using place-value numeric representation.

Most of the time, we work with base ten (decimal) numbers. So numbers like 2007 are understood to be in base ten, and we don't need to write it as 200710. Thus, each "place" represents a different power of ten:

2007 = 200710 = (2 x 103) + (0 x 102) + (0 x 101) + (7 x 100).

Sometimes we write things in other bases. Computers operate in binary, which is base 2. Each wire either has voltage (1) or doesn't (0). So it works with just the digits 0 and 1 (2 digits, hence "base 2"). Example:

100112 = (1 x 24) + (0 x 23) + (0 x 22) + (1 x 21) + (1 x 20).

Octal is base 8, so only the digits 0-7 are allowed:

7128 = (7 x 82) + (1 x 81) + (2 x 80).

Larger bases, like Hexadecimal (base 16) are often used with computer programming. In such cases, we use alphabetics to extend the available digits. So we have 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, D, C, D, E, F (a total of 16 "digits"). Example:

9EA216 = (9 x 163) + (14 x 162) + (10 x 161) + (2 x 160).

Any given value can be expressed in any base. All the following are equal to 2007:

2007 = 200710 = 7D716 = 37278 = 111110101112.

Hope this helps,
Stephen La Rocque.

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