IPA FE Subject A 2023 Question 1
A question IPA Japan published in 令和５年度 基本情報技術者試験 科目A 公開問題 問1, translated into English. ITPEC is based on the same exams.
Which of the following is the result of converting the hexadecimal fraction 0.C into a decimal fraction?
Explanation
0.75 — the first hexadecimal digit after the point is worth 1/16, so 0.C is C ÷ 16.
In hexadecimal the places after the point have the weights 16−1, 16−2, and so on. The digit C stands for 12, so 0.C = 12 × 1/16 = 12 ÷ 16 = 0.75.
Check through binary, four bits per hexadecimal digit: C is 1100, so 0.C is the binary fraction 0.1100 = 0.5 + 0.25 = 0.75.
Answer (c)
Why not others:
- •(a) 0.12 — reads C as the decimal number 12 and writes it after the point, as if the place were worth 1/100 instead of 1/16
- •(b) 0.55 and (d) 0.84 — one hexadecimal digit after the point always gives a multiple of 1/16 = 0.0625 (0.5, 0.5625 … 0.8125, 0.875), and neither value is one
Key rule: The k-th hexadecimal digit after the point is worth 16−k; rewriting each digit as four bits and adding the binary weights is a quick check.
Basic Theory · AI-written, may contain errors
This question comes from the past questions IPA Japan publishes, translated into English by ITPEC Practice. ITPEC Practice is an independent study tool and is not affiliated with IPA or ITPEC. See the original paper (PDF) or Report an issue.