Arithmetic of Computers

Arithmetic of Computers

from Tenscope Limited

Lesson 7

Decimals to Octals

. . . and back again

Page 241

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Your answer :
.110 = .0631463148.
You are correct. Beastly thing won’t stop, will it? Just as we have recurring decimals, such as (1)/(3) = .3333⋯, (1)/(7) = .142857142⋯, we have recurring octal fractions. The curious thing is that all multiples of .110 (except .510 = (1)/(2) = .48) expressed in the octal system contain the repeating digits 6314.
.110  = .06314631468 .210  = .14631463148 .310  = .23146314638 .610  = .46314631468 .910  = .71463146318
Many octal fractions do not terminate in zeros, so we must face up to the problem of rounding octal fractions. How would you round 21.448 to the nearest (octal) number?
Answer :
21.448 rounds to 218.

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21.448 rounds to 228.

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