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You are exactly right. The octal number 2138 is the shorthand way of writing
2(82) + 1(81) + 3(80)
just as the decimal number 64310, for example, is the shorthand way of writing
6(102) + 4(101) + 3(100).
We do not usually write the subscript 10 on a decimal number, such as 64310, because ordinarily we use only decimal numbers. However, in the rest of this book, we shall use the subscript 10 wherever confusion might otherwise arise.
Now, the position of each digit in an octal number tells us which power of 8 that digit multiplies, just as in the decimal system, where the position tells us which power of 10 a particular digit multiplies. The right-hand digit in a whole octal number is the coefficient of 80, the next digit to the left is the coefficient of 81, and so on.
In the octal number 3468, what is the coefficient of 80?
