IB Computer Science: Binary Essentials | 二进制考点精讲

📚 IB Computer Science: Binary Essentials | 二进制考点精讲

Binary is the fundamental language of computers. In IB Computer Science, understanding binary representation, arithmetic, negative number encoding, floating-point numbers, and logical operations is essential for scoring well on Paper 1 and Paper 2. This revision guide distills the key concepts you must master, with clear explanations and examples.

二进制是计算机的基础语言。在IB计算机科学中，理解二进制表示、算术运算、负数编码、浮点数以及逻辑运算是Paper 1和Paper 2拿高分的关键。这篇考点精讲提炼了你必须掌握的核心概念，并配有清晰的解释和示例。

1. What is Binary? | 什么是二进制？

A binary number system uses only two digits: 0 and 1. Each digit is called a bit (binary digit). Computers use binary because digital circuits have two stable states (on/off), representing 1 and 0. A group of 8 bits forms a byte, which is the basic unit of storage.

二进制数字系统只使用两个数字：0和1。每个数字称为一个二进制位（bit）。计算机使用二进制是因为数字电路有两种稳定状态（开/关），代表1和0。8个位组成一个字节（byte），这是存储的基本单位。

In the binary place-value system, each position represents a power of 2. The rightmost bit is the least significant bit (LSB, 2⁰), and the leftmost bit is the most significant bit (MSB). For example, the binary number 1101₂ is calculated as: 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 13₁₀.

在二进制位值系统中，每一位代表2的幂次。最右边的位是最低有效位（LSB, 2⁰），最左边的位是最高有效位（MSB）。例如，二进制数1101₂计算为：1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 13₁₀。

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

To convert a binary integer to decimal, multiply each bit by its place value (power of 2) and sum the results. For fractional binary numbers, bits after the binary point represent negative powers of two: 2⁻¹ = 0.5, 2⁻² = 0.25, and so on.

要将二进制整数转为十进制，将每个位乘以其位值（2的幂）然后求和。对于带小数的二进制数，二进制小数点后的位表示2的负幂：2⁻¹ = 0.5，2⁻² = 0.25，依此类推。

Example: Convert 1011.01₂ to decimal.

示例：Published by TutorHao | IB Computer Science Revision Series | aleveler.com