Arithmetic of Computers

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Lesson 6

The Octal System

From eight to ten

Page 216

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Your answer :

20₈.

You are correct. Since 7 is the largest single numeral in the octal system, the number following 17₈ must be 20₈. We can always check this by expanding the octal numbers and converting to decimal:

17₈ = 1(8¹) + 7(8⁰) = 1(8) + 7(1) = 15₁₀; 20₈ = 2(8¹) + 0(8⁰) = 2(8) + 0(1) = 16₁₀.

So the octal numbers 17₈ and 20₈ correspond to the decimal numbers 15₁₀ and 16₁₀ respectively.

Now we can count in octal as follows:

0₈, 1₈, ⋯, 7₈, 10₈, 11₈, ⋯, 17₈, 20₈, 21₈, ⋯, 30₈, ⋯, 40₈, ⋯, 50₈, ⋯, 60₈, ⋯, 70₈, ⋯, 77₈, ⋯,

where the dots stand for numbers that we aren’t taking the space to write, since you can see how to fill in the blanks for yourself.

How shall we get the next number beyond 77₈ in the octal system?

In other words, what is 77₈ + 1₈?

Answer :

77₈ + 1₈ = 78₈.