The half-life is simply the amount of time it takes for half of the isotope to decay into something else.
After 1 half-life, half of the original sample remains. After a second half-life, half of that part remains or 1/4 of the original....after 3 half-lives, 1/8 remains and so on.
In your example, ut started with 8 billion atoms. After one half-life, there was 4 billion. After a second half-life, there was 2 billion and after 3, one billion remain.
