Arithmetic of Computers

Arithmetic of Computers

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Lesson 7

Decimals to Octals

. . . and back again

Page 242

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Your answer :
3.
You are correct. The number 3.14 is said to have an integral part, 3, and a fractional part, .14. The word “integral” comes from the word “integer,” which is another name for a whole number.
With these names for the parts of a number we can show you a method for converting decimal fractions to octal fractions. We converted decimal whole numbers to octal whole numbers by repeated division by 8. To convert fractions we use repeated multiplication by 8. Again, the method is best explained by an example. Consider the conversion of .437510 which is (7)/(16), to an octal number, as shown below:
FIRST STEP: Multiply .4375 by 8:
.4375  ×  8 integral part,  1st product →  3.5000  ← fractional part,  1st product
SECOND STEP: Multiply only the fractional part of the 1st product by 8 again:
3.5000  ← fractional part,  1st product  ×  8 integral part,  2nd product →  4.0000  ← fractional part,  2nd product
The fractional part of the 2nd product is 0, which tells us that the conversion is finished. The digits of the octal fraction equal to .437510 are the integral parts of the successive products, written in the order obtained.
Thus,
Answer :
.437510 = .438.

Go to Page 239

.437510 = .348.

Go to Page 255


Answer to Self-Test Question 5, Lesson 7 :
a. .18; b. .018.

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