information theory is hard let's go shopping

that does not make sence!

ok lets look at audio using binary as everything in computing is based on binary.

lets for a moment assume the following binary is a wave file.

original wave = 101001000011110100101010010011010101001010

i understand that its way too small to be a wave file but lets just say it is for a moment!

after compression lets assume the following is the mp3 binary

compressed mp3 = 1010010

this should then leave you with the following leftover wave binary

leftover or disgarded wave information = 00011110100101010010011010101001010

why is it not possible to add the mp3 binary with the disgarded wave to recreate the original file again? like so

1010010 + 00011110100101010010011010101001010