問91
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2進数1011と2進数101を乗算した結果の2進数はどれか。
平成28年度 秋期 ITパスポート試験 問91
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 91
Incorrectア
1111 is 15 in decimal. It is not even the sum of 11+5; it merely has 4 digits so it looks close to the correct answer, but as a multiplication result the value is too small and does not equal 11×5=55.
Incorrectイ
10000 is 16 in decimal. This is exactly 11+5=16, i.e. the result of adding the two numbers. Since the question asks for multiplication, it is wrong. This option is designed to trap those who confuse addition with multiplication.
Incorrectウ
101111 is 47 in decimal (=32+8+4+2+1). It is close to the correct answer 55, but it is a value that easily arises when you make a mistake with a carry or a shift position in the long multiplication, and it does not equal 11×5=55.
- エ
正解 Binary multiplication works with the same long-multiplication idea as decimal. First convert both numbers to decimal: 1011 is 8+2+1=11, and 101 is 4+1=5. The product is 11×5=55. Converting 55 back to binary, 55=32+16+4+2+1=110111, so エ is correct. Doing the long multiplication directly in binary gives the same result: 1011×1=1011; the next digit is 0, so 0000; the top digit is 1, so shift 1011 left by 2 places to get 101100. Adding these, 1011+101100=110111, which matches.
ここがポイント
- Binary multiplication can be found either by converting to decimal, computing, and converting the result back to binary, or by long multiplication directly in binary—shifting each digit left and adding.
- Basics of positional notation: each binary digit has a weight of 16, 8, 4, 2, 1 counting down from the higher positions. As in 110111=32+16+4+2+1=55, you can convert to decimal by summing the weights.
用語