Properties of Numeric Codes Sequential, Self Complementing, and Cyclic Codes || Lesson 29 ||

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Here we will try to understand Properties of Numeric Codes Sequential, Self Complementing, and Cyclic Codes.

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The discussion about the classification of Binary codes and the classification of Numeric codes will help you understand the properties of numeric codes.

Properties of Numeric Codes Sequential, Self Complementing, and Cyclic Codes:

The image below is the classification of the binary codes.

From the above image, we have some of the numeric codes.

Within those codes some properties are hidden.

There are three properties for the numeric codes.

1. Sequential Codes

2. Self Complementary Codes

3. Cyclic Codes

Sequential Codes:

Sequential code is one in which each succeeding codeword is one binary number greater than its preceding codeword.

The numeric code is said to be sequential if we consider any two codes in sequence the succeeding code is one binary number greater.

From the above numeric codes 8421 and XS-3 codes are sequential.

Self Complementary Codes:

A code is self-complementary if the code word of the 9’s complement of N i.e. of 9 – N can be obtained from the code word of N by interchanging all 0’s and 1’s.

For example, if we take any codeword 0001 ( N ) of 2421 coding mechanism if the codeword obtained by the 9’s complement of N which is 9 – 1 = 8 if the codeword of 8 is obtained by the complement of N then those kinds of codewords are called self complementing codes.

From the above numeric codes 2421, 5211, 642-3, 84-2-1 are self complementing codes.

Cyclic Codes:

Cyclic codes are those in which each successive codeword differs from the preceding one in only one-bit position.

From the above code words none of the codes are cyclic codes.

Gray codes are cyclic codes.

We will have a clear understanding of cyclic codes when we discuss gray codes.

For now, we will take a sample codewords in the sequence of the Gary codes.

The codes are 0101 representing decimal number 6 and 0100 representing decimal number 7.

If we closely observe the codes in both the codes only one bit is differing and that bit is in the 0th position.

Similarly, if we consider any two codes in Gray there will be the only 1-bit difference.

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