The letters A, G, C, and T represent the four nitrogen bases of which make up the different proteins responsible for the unique characteristics found in each and every one of us, these letters are a man made interpretation of what we believe make up the DNA helix, this is not GOD's math but man's effort to understand these complexities, we don't even know for sure if it is actually 100% accurate or complete, but evidence would suggest it's a good start. The image we know of a double helix is also but a guess.
binary code or the one's and zero's represent off and on routines, 1 being "on" and 0 being off, the "and" or "or" sequences are that of combinations of "off and on" values as is the same with "yes or no" or negative and positive you only get 2 choices in binary duality. In binary language the zero is not represented as a value and is null, only the 1 represents a value or positive.
the two examples "DNA and Binary code" have absolutely no correlation or resemblance between one another, relating the two is like saying that the rings in a tree are in direct correlation to the RPM's in a cars engine! they are both a count of progression or a number but that's where the similarities stop!