And true the most important or consuming area is the digital back.
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A digital back draws only a near-infinitesimal amount of power from the Contax body, attributable to the line drivers on the camera side of the interface connector. This is in contrast to a film back, whose motor is the main consumer of the body's battery power.
I don't know the maximum current draw of the Contax. ToCAD America (still providing some measure of support until 2015) may be able to tell you. The nominal supply voltage is 6V, use a supply with good voltage regulation.
-H.