Note In modulo-N arithmetic,we use only the integers in the range 0 to N-1,inclusive. 在模N运算中，只使用0到N-1的整数 10.11
10.11 In modulo-N arithmetic, we use only the integers in the range 0 to N −1, inclusive. 在模N运算中，只使用0到N-1的整数 Note
Figure10.4 XORing of two single bit讴or two words模2运算和异或运算关系 0⊕0=0 1④1=0 10110 a.Two bits are the same,the result is 0. ⊕ 1 1 1 0 0 01 0 0 1 0①1=1 1①0=1 b.Two bits are different,the result is 1. c.Result of XORing two patterns 10.12
10.12 Figure 10.4 XORing of two single bits or two words 模2运算和异或运算关系
1O-2 BLOCK CODING块编码 In block coding,we divide our message into blocks, each of k bits,called datawords.We add r redundant bits to each block to make the length n =k r.The resulting n-bit blocks are called codewords. 在块编码中，我们把报文创分成块，每块位，称数据字， 并增加r个冗余位使其长度变为n=k+r,形成n位块称为码字。 Topics discussed in this section: Error Detection 检 Error Correction 纠错 Hamming Distance 汉明距离 Minimum Hamming Distance最小汉明距离 10.13
10.13 10-2 BLOCK CODING 块编码 In block coding, we divide our message into blocks, each of k bits, called datawords. We add r redundant bits to each block to make the length n = k + r. The resulting n-bit blocks are called codewords. 在块编码中，我们把报文划分成块，每块k位，称数据字， 并增加r个冗余位使其长度变为n=k+r，形成n位块称为码字。 Error Detection 检错 Error Correction 纠错 Hamming Distance 汉明距离 Minimum Hamming Distance 最小汉明距离 Topics discussed in this section:
Figure10.5 Datawords and codewords in block coding数据字和码字 k bits k bits k bits 2k Datawords,each of k bits n bits n bits n bits 2 Codewords,each of n bits(only 2k of them are valid) 10.14
10.14 Figure 10.5 Datawords and codewords in block coding 数据字和码字
Example 10.I The 4B/5B block coding discussed in Chapter 4 is a good example of this type of coding.In this coding scheme, k 4 and n 5.As we saw,we have 2k 16 datawords and 2n 32 codewords.We saw that 16 out of 32 codewords are used for message transfer and the rest are either used for other purposes or unused. 第四章讨论的4B5B码就是这种编码的一个好例子。我 们可以看到，由于k=4,=5,刚数据字有2k=16个， 码字有2”=32个。我们从32个码字里精心挑选16个码 字用于报文传输。其余16个不用。 10.15
10.15 The 4B/5B block coding discussed in Chapter 4 is a good example of this type of coding. In this coding scheme, k = 4 and n = 5. As we saw, we have 2 k = 16 datawords and 2 n = 32 codewords. We saw that 16 out of 32 codewords are used for message transfer and the rest are either used for other purposes or unused. 第四章讨论的4B/5B码就是这种编码的一个好例子。我 们可以看到，由于k=4，n=5，则数据字有2 k = 16 个， 码字有2 n = 32 个。我们从32个码字里精心挑选16个码 字用于报文传输。其余16个不用。 Example 10.1