Shooting began in London this week.
Turing's work at Bletchley Park was credited with cracking the German Enigma Code, a key part of the Allies' victory in the Second World War.
He was prosecuted for gross indecency over homosexual acts.
Benedict will also soon be seen as WikiLeaks founder Julian Assange in The Fifth Estate.
And as the voice of Smaug the dragon in The Hobbit: The Desolation Of Smaug.
And also as some fictional detective or other.