Arithmetic of Computers

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Lesson 6

The Octal System

From eight to ten

Page 209

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Your answer :

13.4₈ = 11.5₁₀.

You are correct. An octal fraction such as .762₈ can be converted to a decimal fraction by writing the number in expanded form, as shown below. (We always write the expanded form of a number with decimal numerals, for no particular reason other than the fact that decimal numerals are familiar and therefore convenient to work with.)

.762₈ = 7(8^− 1) + 6(8^− 2) + 2(8^− 3) = 7⎛⎝(1)/(8¹)⎞⎠ + 6⎛⎝(1)/(8²)⎞⎠ + 2⎛⎝(1)/(8³)⎞⎠ = 7⎛⎝(1)/(8)⎞⎠ + 6⎛⎝(1)/(64)⎞⎠ + 2⎛⎝(1)/(512)⎞⎠.

Now, as you can see, the arithmetic is going to get a little sticky here:

(1)/(8) = .125₁₀; (1)/(64) = .015625₁₀; (1)/(512) = .001953125₁₀.

Our sum is actually .97265625₁₀ = .762₈.

Now it’s your turn. Convert .54₈ to a decimal fraction by expansion.

Answer :

.54₈ = (44)/(64).