I think cycle = on your period.
yes, you can get pregnant if you have unprotected sex when on your period. Sperm can last up to 5 days, and you can easily ovulate in time for the sperm and egg to meet up.
However, if you're on birth control pills and you're taking them properly than the chance that you can get pregnant while on your inactive (bleeding) days is less than 1%, same as the weeks when you're on the pill.