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# Run length encoding of a bit sequence

(a) Encode the following bit sequence using run-length encoding with 4-bit codes

eighteen zeroes, 11, fifty-six zeroes, 1, fifteen zeroes, 11.

(b) Encode the same sequence using run-length encoding with 5-bit codes

(c) Compare the two codes. Comment on two choices.

#### Solution Preview

In run length encoding (RLE) we normally represent each subsequence of identical symbols by a pair (L,S), where L indicates the length of the subsequence and S indicates the recurring symbol in the sequence. So the encoded sequence will look like -

(L1,S1), (L2,S2), ......, (Ln,Sn)

where two consecutive symbols Si and Si+1 will not be same.

In case of binary sequence, only symbols are 0 and 1. Hence Si will alternate between 0 and 1, which simplifies our RLE sequence to

L1, L2, ...., Ln

However we can't use this simplified representation either in case (a) or ...

#### Solution Summary

Solution also discusses two representations for Run Length Encoded sequences and illustrates a scheme to generate the encoded bit sequence with the help of an example.

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