Bernard was given a lethal injection at Terre Haute, Indiana, prison. This is where most federal death sentences are carried out. In the US, states can carry out the death penalty (about half of the states have it), but the federal government can do that too.
However, that had not happened since 2003, under President Bush. One of the last death sentences carried out was the execution of Timothy McVeigh, the perpetrator of the 1995 Oklahoma City bombing that killed 168. President Trump resumed the practice in July this year. After Bernard, 4 more are planned. That would bring the total since July to 13.
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