If X were a female slave, and the state in which she bore a child had either a "one drop rule" or a less severe law (one-fourth of slave ancestor=slave, for instance), how exactly was the "math" done?
I've encountered a "bug": if the offsprings between X and a free(d)man were considered slaves in a slave state, were said offsprings "100% pure slaves?" If so, does that mean ALL descendants of slaves are forever slaves (since one person can only be either 100% free or 100% slave?)
In short - Slavery had nothing to do with blood quantum, only the status of the mother.
In 1656 a woman named Elizabeth Key Grinstead sued for freedom. She was enslaved, but had been born of the rape of her enslaved mother, and her free Englishman father. As English law at the time stated that a person's citizen status descended from the father (pater familias), she won her suit and was freed.
As a direct result of this, the Virginia Assembly passed in 1662 the partus sequitur ventrem (or: That which follows the womb) law, which states that a person's legal status was matrilineal. Eventually, this was adopted by all colonies. Following the American Revolution, this was codified into law such as the law in Louisiana which stated, "Children born of a mother then in a state of slavery, whether married or not, follow the condition of their mother."
In your example, the offspring would be a slave, as the mother was a slave. The status of the father did not matter. This was done primarily for economic reasons, although the obvious connection with the rape of enslaved women likely contributed to it as well.
While you wait for new answers, take a look at this excellent one from /u/secessionisillegal