The BlackMagic Cinema Camera can run a short time with it's internal battery, but it's really designed to use external power. I've shared a few options on this blog, but here's another option to power the BMCC off of a 14V battery adapter using Sony BP-U60 / BP-U30 batteries. If you already have these batteries from your Sony EX-1 camera, this is a great little add-on.
This battery adapter has a 1/4-20 threaded screw to attach to many rigs or cages, or can be mounted to the optional 15mm clamp. If you don't have batteries, you may want to look into the adapter plates that are bundles with a battery charger. You can find these products via eBay following the links (below).