Arithmetic of Computers

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Lesson 7

Decimals to Octals

. . . and back again

Page 255

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Your answer :

.4375₁₀ = .34₈.

You are correct. The process was

.4375 × 8 (Multiply by 8) 1st integral part → 3.5000 × 8 ( Multiply only the fractional part of the first product by 8 again) 2nd integral part → 4.0000

The integral parts of the successive products are the digits of the octal form of the fraction, written in the order obtained, from top to bottom, and we get .4375₁₀ = .34₈.

We can check this, of course. Recall that .4375₁₀ = (7)/(16).

.34₈ = 3(8^− 1) + 4(8^− 2) = 3⎛⎝(1)/(8)⎞⎠ + 4⎛⎝(1)/(64)⎞⎠ = (3)/(8) + (4)/(64) = (24)/(64) + (4)/(64) = (28)/(64) = (7)/(16).

Now convert .6328125₁₀ into an octal fraction.

Answer :

.6328125₁₀ = .54₈.