Hanged and hung both are past participles and past tenses of the verb to hang but they are used in different contexts.
Hanged is restricted to the sense of hang that means to suspend by the neck until dead, or to put to death by hanging.
- He was hanged for murder.
- She hanged herself moments after the result was announced.
- A few hours after he was hanged, the terrorist's body was buried at the central jail.
- They hung the picture on the wall by the door.
- A towel hung from the the rail.
- I hung my daughter's picture above my working desk.