Hung is the past tense and past participle of hang in most of that verb’s senses. For instance, yesterday you might have hung a picture on the wall, hung a right turn, and hung your head in sorrow. The exception comes where hang means to put to death by hanging. The past tense and past participle of hang in this sense, and only in this sense, is hanged.
When someone is hung out of malice but with no intent to kill, as described in the example below, hung is the conventional word:
They hung him by chains and tortured him.
~source: grammarist.com
To be executed via noose the ONLY correct word is HANGED.
Past tense, present tense or future tense, it is ALWAYS hanged.
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