I am studying about DNA compression algorithm because it is expected that the dna data will be enormous and increase. The other day, I get a DNA data in fasta format. The data is about 2GB. But I realized. Fasta format is written 'A','T','G','C' by character code. So it takes 8bit per ATGC. But they can be expressed 2bit by binary code. for instance, A=00, T=01, G=10, C=11 To use binary format will reduce its redundancy and be able to storage much smaller size. I think using binary format is better way than using character code.
Are there special reasons that store using a character code.
So, from looking through the answers, your question is almost a rhetorical (and correct) argument for using binary formats. In fact, binary formats are used in bioinformatics and what you have described is very close to the 2bit format. There are certainly pros and cons, most of which have been described in the answers or the related questions I have linked.
Edit: just one more point against the simplified '2bit' format you describe: A format for storing DNA sequences should support 'N' not to mention other ambiguity codes, because most draft genomes of today contain them. The 'real' 2bit format however can store this information plus additional masking information (http://www.its.caltech.edu/~alok/reviews/blatSpecs.html) via run length encoded meta-data.
There are plenty of binary formats available. Any decent compression algorithm will generate a binary formatted file. Most people use it for archival purpose mainly. Reference base compression is all the rage these days.
For analysis, it's just simpler to use standard string formats. Being able to manipulate files with simple *nix commands is worth the file size.
I was always thinking the same, one main problem is I guess for variants like W (A/T) when we go for consensus, variant caller. But I guess if we go to binary, we have to accomodate two different (or three) bases some way.
See also: Big data: storage and analysis, Using HDF5 to store bio-data, Data too big to be stored in memory: common options