📚 Data Transmission Errors: Common Error Detection Methods | 数据传输出错：常见错误检测方法
In digital communication, data is transmitted in the form of electrical signals, radio waves or light pulses. During transmission, noise, interference or hardware faults can cause bits to change from 0 to 1, or vice versa. Such changes are called transmission errors, and detecting them is essential for reliable communication.
在数字通信中，数据以电信号、无线电波或光脉冲的形式进行传输。在传输过程中，噪声、干扰或硬件故障可能导致比特位从 0 变为 1，或从 1 变为 0。这种变化称为传输错误，而检测这些错误对于可靠通信至关重要。
1. Types of Transmission Errors | 传输错误的类型
A transmission error occurs when one or more bits are altered during the journey from sender to receiver. A single-bit error means exactly one bit in a data unit has changed. A burst error means two or more bits in the same data unit have been corrupted, often caused by a sudden electrical spike or physical damage to the medium.
当数据从发送方传输到接收方的过程中一个或多个比特位被改变时，就会发生传输错误。单比特错误（single-bit error）指数据单元中恰好一个比特发生了改变。突发错误（burst error）指同一数据单元中两个或更多比特被破坏，通常由突发的电涌或介质的物理损坏引起。
Error detection methods aim to answer one simple question: 'Has the received data been changed?' Note that most methods detect errors but do not correct them; correction is handled separately, often by retransmission.
错误检测方法旨在回答一个简单的问题："接收到的数据是否被改变？"请注意，大多数方法只能检测错误而不能纠正错误；纠错通常通过重传单独处理。
2. Parity Checking | 奇偶校验
Parity checking is one of the simplest error-detection methods. A single parity bit is appended to a block of data before transmission. The value of this bit is chosen so that the total number of 1s in the block, including the parity bit, satisfies a pre-agreed rule: even parity or odd parity.
奇偶校验是最简单的错误检测方法之一。在传输之前，将一个奇偶校验位（parity bit）附加到数据块上。该校验位的值被设定为使数据块（含校验位）中 1 的总数满足预先约定的规则：偶校验或奇校验。
With even parity, the parity bit is set to 0 if the data already has an even number of 1s, and set to 1 if it has an odd number of 1s, making the total always even. With odd parity, the rule is reversed so the total number of 1s is always odd.
在偶校验（even parity）下，如果数据本身有偶数个 1，则校验位设为 0；如果有奇数个 1，则设为 1，使得总数始终为偶数。在奇校验（odd parity）下，规则相反，使 1 的总数始终为奇数。
Consider the data 1010001, which contains three 1s. Using even parity, the parity bit is 1, giving the transmitted 8-bit unit 11010001, with the parity bit placed first. If a single bit flips during transmission, the receiver counts the 1s and finds an odd number, immediately detecting that an error has occurred.
考虑数据 1010001，其中包含三个 1。使用偶校验时，校验位为 1，得到传输的 8 位单元 11010001（校验位放在首位）。如果传输中有一个比特位翻转，接收方统计 1 的个数会发现是奇数，从而立即检测到发生了错误。
The major limitation of parity checking is that it can only detect an odd number of bit changes. If two bits flip simultaneously, the parity remains correct and the error goes completely unnoticed.
奇偶校验的主要局限在于它只能检测奇数个比特位的变化。如果两个比特同时翻转，奇偶性保持不变，错误将完全无法被发现。
3. Checksum | 校验和
A checksum is a more powerful error-detection technique. The data to be transmitted is divided into blocks of equal size, often of 8 or 16 bits. These blocks are then added together using binary arithmetic, and the resulting sum, known as the checksum, is transmitted alongside the data.
校验和是一种更强大的错误检测技术。待传输的数据被分成大小相等的块，通常为 8 位或 16 位。然后使用二进制算术将这些块相加，得到的和称为校验和（checksum），与数据一起传输出去。
Upon receiving the data, the receiver performs the same calculation: it divides the received data into blocks and adds them together. If the calculated sum matches the received checksum, the data is considered valid; if it differs, an error has been detected.
接收方收到数据后执行相同的计算：它将接收到的数据分成块并相加。如果计算得到的和与收到的校验和一致，则数据被认为有效；如果不一致，则检测到错误。
0010111 after discarding the carry. This value 10010111 is the checksum transmitted with the data.
假设发送三个 8 位块：10110011（十进制 179）、01010101（十进制 85）和 10001111（十进制 143）。它们的和为 179 + 85 + 143 = 407，在 8 位算术中舍弃进位后为 10010111（十进制 151）。这个值 10010111 就是随数据发送的校验和。
Checksums can detect burst errors and any combination of bit flips that changes the arithmetic sum. They cannot guarantee detection if the errors happen to cancel out mathematically, but in practice the probability of this is very low.
校验和能够检测突发错误以及任何改变算术和的比特翻转组合。如果错误在数学上恰好相互抵消，校验和无法保证检测出来，但在实际中这种概率非常低。
4. Check Digit | 校验位
A check digit is a single digit added to a number, calculated from the other digits
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