There are 10 prisoners to be executed. So the emperor can make them taste wine from the barrels.
There are 2 possibilities associated with a prisoner when he tastes wine from a barrel - either he dies or he will not die.
So, in a 2 barrel scenario, using a single prisoner, we can identify whether the wine is poisoned or not.
i.e, he will taste bottle 1 and does not taste bottle 2. If he dies then bottle 1 is poisoned and if he survives bottle 2 is poisoned.
Now lets consider the scenario with 2 prisoners, the number of possible combinations would be 2*2 as there are 2 possibilities associated with them.
Barrel 1 -> Tasted by none
Barrel 2 -> Tasted by 1st prisoner
Barrel 3 -> Tasted by 2nd prisoner
Barrel 4 -> Tasted by both prisoners
So, if no one dies, bottle 1 is poisoned, if both of them dies bottle 4 is poisoned.
If prisoner 1 dies Barrel 2 is poisoned. If prisoner 2 dies Barrel 3 is poisoned.
Similarly, when you consider 10 prisoners, the number of possible combinations would be:
2*2*2*2*2*2*2*2*2*2 = 2^10 = 1024.
So, that is sufficient for testing 1000 barrels of wine.
Further you can eliminate the case in which every prisoner has to taste the wine, then 10 possibilities in which 9 of them has to taste the wine and few of the possibilities in which 8 of them has to taste the wine.
So, maximum number of prisoners that will die on tasting the wine is 8.