The decimal number system uses the characters 0, 1, 2, ..., 9 and the octal number system uses the characters 0, 1, 2, ....

Question

The decimal number system uses the characters 0, 1, 2, ..., 9 and the octal number system uses the characters 0, 1, 2, ..., 7. For example, the decimal number 12 (= 1 x 8^1 + 4 x 8^0) is expressed as 14 in the octal number system. The decimal number 108 in the octal number system is:

A. 104
B. 128
C. 150
D. 154

Accepted Answer

(154)_8 = 108_10. Answer D. To convert a decimal number to octal, we repeatedly divide by 8 and collect remainders from bottom to top. The decimal number 108 needs to be expressed using only digits 0-7, where each digit position represents a power of 8 (units, eights, sixty-fours, etc.).