Discussion
The octal number 17 is equivalent to which decimal value?
Answer: B
Correct answer: 15
Octal is base 8, so each digit carries a place value that is a power of eight. For 17 that gives \[ 1 \times 8 + 7 = 15. \] The trap is reading the numeral as though it were decimal, which is why 17 is offered as a distractor. Octal uses only the digits 0 to 7; the digits 8 and 9 do not exist in it, so a numeral containing either is not a valid octal number at all - a quick way to spot a bad option. Octal is used as shorthand for binary because each octal digit corresponds to exactly three bits: 1 is 001 and 7 is 111, so 17 in octal is 001111, which is 15. Conversion is done by grouping bits in threes from the right, with no arithmetic. It was common on machines with word lengths divisible by three, and survives in Unix file permissions, where 755 and 644 are octal.
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