I should have added that Saddamn's designers probably had the advantage of access to Pakistani and other designers, possibly even some hungry Russian ones. Maybe Chinese too. Also they may have had access to all sorts of information from the US program, via the Chinese or others.
The hard part is not making the bomb, the hard part is getting or producing the weapons grade uranium or the plutonium.
The weapons-grade nuclear material is THE hard part, but given modern designs, getting the explosives to implode just so is a close second with or without computers.