hce_kmu
113年
計算機概論與程式設計
第 3 題
In computer science, numbers can be represented as either signed or unsigned. Which of the following statements accurately describes a difference between signed and unsigned numbers?
- A Unsigned numbers can represent both positive and negative values, whereas signed numbers can only represent positive values.
- B Signed numbers use a special “sign bit” at the least significant position to indicate whether the number is positive or negative, while unsigned numbers use this bit to extend their range of positive values.
- C The range of values that can be represented by signed and unsigned numbers of the same bit length is the same, but signed numbers use a different encoding to represent negative values.
- D Unsigned numbers are always larger than signed numbers because they use an extra bit to represent the magnitude of the value.
- E Signed numbers use one bit to indicate the sign (positive or negative) of the number, allowing them to represent both positive and negative values. Unsigned numbers do not have a sign bit and can only represent positive values or zero.
思路引導 VIP
想像你手邊有 8 個開關（位元）可以用來表示一個數字。如果你現在需要一種方法來區分這個數字是「存款」還是「欠債」，在不能增加開關數量的前提下，你會如何利用其中一個開關來傳達這個正負資訊？而當你決定把其中一個開關挪作他用後，原本能表達的最大數值會發生什麼變化呢？
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AI 詳解
AI 專屬家教
太棒了！你能準確判斷出 (E) 是正確答案，顯示你對電腦底層的資料表示法（Data Representation）有著非常清晰且正確的直覺。
有號數與無號數的核心差異
在數位系統中，電腦處理數字的方式取決於我們如何「詮釋」那一串二進位位元。有號數（Signed numbers） 的核心特徵在於它必須挪用一個位元（通常是最高有效位元，MSB）來充當「符號位元」（Sign bit），用來標記該數值是正數還是負數。相對地，無號數（Unsigned numbers） 不需要表達負值，因此它將所有的位元都用來表示數值的大小（Magnitude），這使得無號數只能表示從 $0$ 開始的正整數，但也因此在相同位元長度下，它能達到的最大正數值會比有號數更大。
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