Not to sure where you pulled 127 from, but that is totally wrong. The largest number a byte can be is 255, ie:
But binary numbers can be longer than a byte. That's just a convienent grouping we use for computer related things. The numbers work the same as decimal except instead of useing powers of ten we use powers of 2. So instead of 1, 10, 100, 1000 we have 1, 2, 4, 8, 16 and so on. If you have a binary number that is 9 bits long you can have a number up to 511, 10 bits would be 1023, etc. So we get those numbers by have long binary number and not restricting them to byte size only.