001101100011010101001001001101000001010010110010110

The result looks like this:

,0,01,1,011,00,0110,10,101,001,0010, 01101,000,00101,001011,0010110

Since we will code the prefix number using the same 0s and 1s that also occur as characters in the string, we need our coded strings to have a fixed length. Since we have 16 strings (counting also the first "empty" string, which will be given the position number "zero"), we will need 4 bits for numbering them in binary. As we number the strings, starting from the first non-empty string (see Position Number in the table below), we also check what the Prefix is (that is the piece of the string before its last digit) and the Position Number of that prefix (which, by construction, is a string that was encountered before). The coded string is then constructed by taking the Position Number of the Prefix, and following that by the last bit of the string that we are considering.

This table shows the proper method for encoding. Fill in the empty slots:

Practice
Coding Individual Strings for Binary Version of Lempel-Ziv Algorithm

The LZ-coded version of the chain in this example is then formed by writing all the coded strings (from the last column in the table) in one long chain.
In our example, the original string of:

001101100011010101001001001101000001010010110010110

becomes:

0000000011000010010100010010000011001111
01011100100100101010101011101111101