GCSE WJEC Computer Science: Calculation Practice | GCSE WJEC计算机科学：计算题专项训练

📚 GCSE WJEC Computer Science: Calculation Practice | GCSE WJEC计算机科学：计算题专项训练

Mastering calculations is vital for the WJEC GCSE Computer Science exam. This guide provides focused practice on the most common calculation-based questions, from number conversions to file sizes, Boolean logic, CPU performance, and networking. Each section explains the concept with a worked example, followed by step-by-step solutions.

掌握计算题对WJEC GCSE计算机科学考试至关重要。本指南针对最常见的计算类题型进行专项训练，涵盖数制转换、文件大小、布尔逻辑、CPU性能和网络等。每个小节先讲解概念并给出示例，再逐步展示解答过程。

1. Number System Conversions | 数制转换

The ability to convert between binary, denary, and hexadecimal is fundamental. You must be able to quickly and accurately change a number from one base to another.

二进制、十进制和十六进制之间的转换是一项基本技能。你必须能快速准确地将一个数字从一种进制转换为另一种。

Denary to Binary: Repeatedly divide by 2, recording the remainders. Read from bottom to top.

十进制转二进制： 反复除以2，记录余数，从下往上读。

Example: Convert 53₁₀ to binary.

示例：将 53₁₀ 转换为二进制。

53 ÷ 2 = 26 r 1, 26 ÷ 2 = 13 r 0, 13 ÷ 2 = 6 r 1, 6 ÷ 2 = 3 r 0, 3 ÷ 2 = 1 r 1, 1 ÷ 2 = 0 r 1. Reading remainders: 110101₂.

53 ÷ 2 = 26 余 1，26 ÷ 2 = 13 余 0，13 ÷ 2 = 6 余 1，6 ÷ 2 = 3 余 0，3 ÷ 2 = 1 余 1，1 ÷ 2 = 0 余 1。读取余数：110101₂。

Binary to Denary: Sum the place values where there is a 1.

二进制转十进制： 将所有1对应的位权值相加。

Example: 101101₂ = 1×2⁵ + 0×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 32+8+4+1 = 45₁₀.

示例：101101₂ = 1×2⁵ + 0×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 32+8+4+1 = 45₁₀。

Binary to Hexadecimal: Split binary into nibbles (groups of 4 bits), then convert each nibble.

二进制转十六进制： 将二进制分成四位一组，再分别转换每个组。

Example: 11010111₂ → 1101 0111. 1101₂ = D (13), 0111₂ = 7, so D7₁₆.

示例：11010111₂ → 1101 0111。1101₂ = D (13)，0111₂ = 7，结果为 D7₁₆。

Practice converting in all directions; tables can help memorise nibble values.

在转换练习中要多方向练习；表格有助于记住四位二进制对应的值。

2. Binary Addition and Overflow | 二进制加法与溢出

Binary addition follows the same principle as denary addition but uses only 0 and 1. Overflow occurs when the result of an addition exceeds the number of bits available to represent the number, which can lead to errors.

二进制加法遵循与十进制加法相同的原则，但只使用0和1。当加法结果超出用于表示数字的可用位数时，就会发生溢出，这可能导致错误。

Rules: 0+0=0, 0+1=1, 1+1=0 carry 1, 1+1+carry=1 carry 1.

规则：0+0

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