in reply to 3-byte representation
How many numbers do you have in a file? How many files? How many files can you store on a $65 2-TB drive?
The basic premise of Unix is to store data as text, if at all possible. This makes it simple to process it using utilities you hadn't considered when the file was created.
Your numbers fit in 24 bits, so +/- 8,366,608 ... in fact possibly a smaller range, since you suggest adding a constant to shift the numbers to all-positive. If the numbers are evenly distributed, storing as text requires a separator plus 1-7 digits, plus a possible minus sign. That works out to an average of 5 bytes per number, if you're using ASCII. If there is any asymmetry to make small values more likely than large ones, it might be better than 5 bytes. For a small loss you are now able to feed your files through grep, dc, tr, sed, awk, perl.
As Occam said: Entia non sunt multiplicanda praeter necessitatem.