A-Level OCR Computer Science: Binary In-Depth Revision | A-Level OCR 计算机：二进制 考点精讲

📚 A-Level OCR Computer Science: Binary In-Depth Revision | A-Level OCR 计算机：二进制 考点精讲

In the OCR A-Level Computer Science specification (H446), binary arithmetic is fundamental to understanding how data is represented and manipulated in computer systems. This comprehensive revision guide covers key concepts: from base conversion and binary arithmetic to two’s complement and floating-point representation, ensuring you master every exam requirement.

在 OCR A-Level 计算机科学大纲（H446）中，二进制运算是理解数据在计算机系统中如何表示和处理的基础。本综合复习指南涵盖关键概念：从进制转换和二进制运算到补码和浮点表示，确保你掌握每一个考试要点。

1. Binary Basics and Place Values | 二进制基础与位值

Binary is a base-2 number system using only two digits: 0 and 1. Each position represents a power of 2, increasing from right to left (…, 2³, 2², 2¹, 2⁰). For instance, the binary number 1101₂ equals (1×2³) + (1×2²) + (0×2¹) + (1×2⁰) = 8+4+0+1 = 13 in denary (decimal). The leftmost bit is the most significant bit (MSB), and the rightmost is the least significant bit (LSB).

二进制是以2为基数的数字系统，仅使用0和1两个数字。每个位置代表2的幂，从右向左递增（…、2³、2²、2¹、2⁰）。例如，二进制数 1101₂ = (1×2³) + (1×2²) + (0×2¹) + (1×2⁰) = 8+4+0+1 = 十进制13。最左边的位是最高有效位（MSB），最右边的是最低有效位（LSB）。

A group of 8 bits is called a byte, which can represent values from 0 to 255 in unsigned binary. Understanding place values is essential before tackling conversions or arithmetic.

一组8位称为一个字节，无符号二进制可表示0到255的值。在处理转换或运算之前，理解位值至关重要。

2. Binary to Denary Conversion | 二进制转十进制

To convert an unsigned binary integer to denary, sum the powers of 2 where the digit is 1. For 10110₂: 1×2⁴ + 0×2³ + 1×2² + 1×2¹ + 0×2⁰ = 16 + 0 + 4 + 2 + 0 = 22. The same method applies to any bit width, such as 8-bit or 16-bit numbers.

要将无符号二进制整数转换为十进制，将所有数字位为1的位置对应的2的幂相加。对于10110₂：1×2⁴ + 0×2<

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