A-Level CCEA Computer Science: Calculation Practice | A-Level CCEA 计算机科学：计算题专项训练

📚 A-Level CCEA Computer Science: Calculation Practice | A-Level CCEA 计算机科学：计算题专项训练

In the CCEA A-Level Computer Science specification, calculation-based questions appear across many topics, from data representation to Boolean logic, data transmission, compression and algorithm analysis. This article provides targeted practice in essential calculation skills, helping students build confidence and accuracy for the exam.

在 CCEA A-Level 计算机科学课程中，计算题遍布数据表示、布尔逻辑、数据传输、压缩和算法分析等多个主题。本文提供针对性的计算技能专项训练，帮助考生提高解题自信和准确率。

1. Number Systems and Conversions | 数制与转换

Understanding binary, denary and hexadecimal conversions is fundamental. Example: Convert the binary number 101101₂ to denary. 1×2⁵ + 0×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 32 + 0 + 8 + 4 + 0 + 1 = 45.

掌握二进制、十进制与十六进制之间的转换是基础。例题：将二进制数 101101₂ 转换为十进制。1×2⁵ + 0×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 32 + 0 + 8 + 4 + 0 + 1 = 45。

Convert denary 198 to hexadecimal: 198 ÷ 16 = 12 remainder 6. 12 is C, so result is C6₁₆.

将十进制 198 转换为十六进制：198 ÷ 16 = 12 余 6。12 为 C，因此结果为 C6₁₆。

Convert hexadecimal 2F to denary: 2×16 + 15 = 32 + 15 = 47.

十六进制 2F 转十进制：2×16 + 15 = 32 + 15 = 47。

2. Binary Arithmetic | 二进制算术

Addition of binary numbers follows column-wise rules, with carries when sum equals 2 (10₂). For example, add 1011₂ (11) and 1101₂ (13):

二进制加法遵循逐位相加原则，当和等于 2（即 10₂）时产生进位。例如计算 1011₂（11）加 1101₂（13）：

1011
+ 1101
——
11000₂ (24)

1011
+ 1101
——
11000₂ (24)

Overflow detection: In an 8-bit register, the addition of two positive numbers can produce a result that exceeds 127, indicated by a sign change. Example: 01111111 (127) + 00000001 (1) = 10000000 (−128 in two’s complement) – overflow occurs.

溢出检测：在 8 位寄存器中，两个正数相加可能产生超过

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