A speech coding algorithm was developed which was based on a new method of selecting the excitation signal from a codebook of residual error sequences. The residual error sequences in the codebook were generated from 512 frames of real speech signals. L.P.C. inverse filtering was used to obtain the residual signal. Each residual error signal was assigned an index. The index was generated using a moments algorithm. These indices were stored on a Graded Binary Tree. A Binary Search was then used to select the correct index. The use of a Graded Binary Tree in the coding algorithm reduced the search time. The algorithm faithfully reproduced the original speech when the test residual error signal was chosen from the training data. When the test residual error signal was outside the training data, synthetic speech of a recognisable quality was produced. Finally, the fundamentals of speech coders are discussed in detail and various developments are suggested.