問79
頻出度★★☆
16進数の A3は10進数で幾らか。
平成24年度 秋期 ITパスポート試験 問79
テクノロジ系基礎理論 › 離散数学
This question's explanation and your answers so far.
解説
問 79
Incorrectア
103 is the value you get by replacing A with 10 and then reading the resulting string directly as a decimal number (A3 → joining “10” and “3” into 103). Radix conversion requires multiplying each digit by its positional weight, so the upper digit 10 must be multiplied by 16. The correct calculation is 10 × 16 + 3 = 163, and 103 is a mistake that ignores the positional weights.
Incorrectイ
153 is the value of 10 × 15 + 3, a mistake that treats the weight of the upper digit as 15 instead of 16. The positional weight in hexadecimal is the radix itself, 16 (16 to the power of 1), while 15 is merely the number corresponding to F, the largest value a single digit can represent. The correct calculation is 10 × 16 + 3 = 163.
- ウ
正解 Hexadecimal is a notation that uses A, B, C, D, E, and F after 0-9 so that a single digit represents 16 values, corresponding to A = 10, B = 11, C = 12, D = 13, E = 14, and F = 15. In a two-digit hexadecimal number each position carries a weight: the upper digit has a weight of 16 to the power of 1 = 16, and the lower digit has a weight of 16 to the power of 0 = 1. Therefore A3 is the upper digit A = 10 multiplied by 16, giving 10 × 16 = 160, plus the lower digit 3 multiplied by 1, giving 3, so 160 + 3 = 163. The correct answer is therefore ウ, 163. As a check in the reverse direction, 163 ÷ 16 = 10 remainder 3, so the quotient 10 is the upper digit (= A) and the remainder 3 is the lower digit, which indeed brings us back to A3.
Incorrectエ
179 is the value of 11 × 16 + 3, a mistake that takes A for 11. In hexadecimal, A comes right after 0-9, so A = 10 and B = 11. If you count the A in the first digit as 11, the correspondence shifts by one all the way along and you get 179, which is larger by 16. Correctly, A = 10, so 10 × 16 + 3 = 163.
ここがポイント
- Hexadecimal is a numeral system in which one digit represents 16 values, corresponding to A=10, B=11, C=12, D=13, E=14, and F=15. Memorizing this correspondence accurately is the first step in radix conversion.
- Converting from base n to decimal is done by taking the sum of “each digit's value × that position's weight”. For a two-digit hexadecimal number the upper weight is 16 to the power of 1 = 16 and the lower weight is 16 to the power of 0 = 1, so A3 = 10 × 16 + 3 = 163.
用語