You are correct, as we can show by expanding the octal number:
118
= 1(81) + 1(80)
= 1(8) + 1(1) = 910.
Let’s look at this another way for a moment. The idea that 7 + 1 = 10, even in the octal system, may take quite a bit of getting used to.
In the decimal system we have just ten symbols to represent different quantities: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. When we count beyond 9, we have no new symbols to use, so we use the same symbols over again by forming combinations of them: 10, 11, 12, 13, etc.
The quantity represented by the decimal digit 8 is the base of the octal system. In the octal system, we use just eight symbols to represent quantities, and we borrow these symbols from our familiar decimal system. They are 0, 1, 2, 3, 4, 5, 6, and 7. We tack on the subscript 8 to indicate octal digits.
When we add one unit to the octal number 78, we again find ourselves without a symbol to represent the new quantity, just as we did when we added on unit to the decimal number 9. So we proceed as we do in the decimal system.
We start by putting together combinations of the symbols we do have at our disposal to indicate these larger quantities. Furthermore, we build our new combinations exactly as we built combinations in the decimal system: by starting with the symbols of lowest value and relating them to each other by position.
Very well, to count in the octal system, we would proceed as follows: 08, 18, 28, 38, 48, 58, 68, 78, 108, 118, 128, 138, 148, 158, 168, 178 . . .
