10 Henry Quastler 



implies that any digit of the symbolic word, considered by itself, does not 

 necessarily represent a given operation. For instance, a set of recognition 

 operations, such as a naturalist's key, could well be arranged as a sequence of 

 binary tests. In such a case one will not always apply the same sequence of 

 tests; in general, the choice of the second test will depend on the outcome of 

 the first, the choice of the third on the outcome of the previous two, etc. 

 Accordingly, the code book will have to specify what operations and what 

 outcomes a particular symbol designates. 



Sequences of code words will represent series of 'events'. Suppose our 

 message were to represent the sequence of events 'G C A'. Using the code given 

 above, we get: 



001101111. 



Observe that the 'words' in the message are not separated by spaces; a space 

 with a defined symbolic meaning (such as a 'whiteness' in the Morse code) 

 would make the alphabet ternary rather than -binary. The receiver will not miss 

 the spaces ; he is expected to know the code and, accordingly, to read the message 

 in groups of three digits, beginning with the first one at the left. 



Any Number of Categories — In general, the number of categories to be 

 encoded is not an integral power of two (such as 2,4,8,16,32 . . .). We could 

 always use the nearest higher power of two as the basis of the coding scheme. 

 For instance, if we had five categories to represent, then we could simply use a 

 portion of our three-digit code for eight categories: 



Category A 1 1 1 



Category B 1 1 



Category C 1 1 



Category D 100 



Category E Oil 



In this example, the symbolization possibilities of the three digits are not 

 fully utilized. This is not economical; one will suspect that it is possible to 

 achieve greater economy in number of digits. This can mean only that some 

 of the five categories will be represented by two digits only. Some words will 

 have two, and some three digits; the decoder will not have the benefit of being 

 able to cut up the message into pieces of equal length. Therefore, it becomes 

 imperative that the words themselves indicate unequivocally the correct partition. 

 This will be the case if no combination of code groups is identical with any 

 other combination of code groups; otherwise, confusion may arise. For 

 instance, the following: 



Category A 1 1 



Category B 10 



Category C 1 



Category D 



Category E 1 1 1 



