Arithmetic of Computers

Arithmetic of Computers

from Tenscope Limited

By using this site, you are accepting "session" cookies, as set out in the site's Privacy Policy
Cookies are also used to remember which page of the book you last viewed, so that when you revisit the site you automatically return to the last page you visited.


Lesson 7

Decimals to Octals

. . . and back again

Page 253

Previous Lesson

Next Lesson

Your answer :
21.448 rounds to 228.
You are correct. 4 occupies the place in the octal system that 5 does in the decimal system; that is, it is half the base of the system; so .48 = (1)/(2) = .510.
Thus .448 is more than (1)/(2). It is actually
(4)/(8) + (4)/(64) = (8)/(16) + (1)/(16) = (9)/(16)
and therefore 21.448 is closer to 228 than to 218.
Most decimal fractions do not produce terminating octal fractions. A safe rule to follow is to keep no more octal places than there are decimal places in the number that was converted, rounding off the octal fraction as appropriate.
Convert .2910 to an octal fraction, rounding the result to 2 octal places.
Answer :
.2910 = .228 (rounded).

Go to Page 234

.2910 = .238 (rounded).

Go to Page 244

Answer to Self-Test Question 6, Lesson 7 :
a. .458; b. .368; c. .668; d. .138.

Return to Self-Test Questions


Previous Page

Next Page