Ivey,
Those Singer machines I have are wired thusly (OEM wiring only);
The 3 pin cord set should have two wires out of it. One side to the power outlet, the other to the controller.
The 2 pin cord set should have a power outlet plug on it.
The block on the machine will have three pins in it regardless. Singer used the same wiring block, just wired it differently.
The wiring for the controller on most cabinet machines comes off the back of the wiring block on the machine, down under the bed of the machine to the controller.
The power cord is removable.
The wiring for the power cord and controller on the portable machines is on the same wire set.
I hope this helps a bit.
Joe