It depends on what you mean by 'describable.' If you are asking, 'can I specify a particular sequence of DNA uniquely using only a sequence of four base pairs?" then the answer is 'yes.' However, based on your second question, I am guessing that's not what you meant.

Given that a cat has been cloned and the clone looks little like its clone (except insofar that both look like cats) I'd say that the determination of how genes operate is still very much a black box. Oh sure, we know about alternative splicing, siRNA, microRNAs, transcription factors, chromatid organization, recombination, etc., but getting from sequence to function is not [yet] fully characterized.