Data Representation: Binary, Hexadecimal & Two’s Complement | 数据表示：二进制、十六进制与二进制补码

📚 Data Representation: Binary, Hexadecimal & Two’s Complement | 数据表示：二进制、十六进制与二进制补码

Data representation is the foundation of all computer science. At AS level Cambridge International (CIE) Computer Science, you must be able to convert between number systems, represent negative integers, perform binary arithmetic and understand how characters are stored. This article covers every core data-representation topic in the AS syllabus, with worked examples and exam-focused explanations.

数据表示是所有计算机科学的基础。在剑桥国际（CIE）AS 计算机科学课程中，你必须能够在不同数制之间进行转换、表示负整数、执行二进制运算，并理解字符的存储方式。本文涵盖 AS 教学大纲中所有核心数据表示主题，附有完整例题和紧扣考点的讲解。

1. Number Systems Overview | 数制概述

A number system is a way of representing values using a fixed set of symbols and positional weights. CIE AS Computer Science examines three systems: denary (base 10), binary (base 2) and hexadecimal (base 16). Denary is the everyday system humans use, with digits 0–9. Binary uses only two digits, 0 and 1, which map directly to the two physical states of a transistor: off and on. Hexadecimal uses sixteen symbols, 0–9 and A–F, and provides a compact notation for binary values.

数制是用一组固定符号和位权来表示数值的方法。CIE AS 计算机科学考查三种数制：十进制（基数为10）、二进制（基数为2）和十六进制（基数为16）。十进制是人类日常使用的系统，数字为0–9。二进制只使用0和1两个数字，直接对应晶体管的两种物理状态：关和开。十六进制使用十六种符号（0–9和A–F），为二进制值提供了简洁的书写方式。

In any positional system, the value of a digit depends on its position. Each position carries a power of the base, working from right to left starting at power zero. As you move left, the positional weight increases by a factor equal to the base.

在任何位权数制中，数字的值取决于它所在的位置。每个位置承载基数的一个幂，从右向左从零次幂开始。越往左，位权按基数倍递增。