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Theoretical design studies of a multilayer hybrid computed tomographic system which could perform both X-ray transmission computed tomography (XCT) and positron computed tomography (PCT) are presented. Use of BGO scintillation crystals makes it possible to achieve the highest spatial resolution and coincident data collection efficiency possible with the present technology. In the new hybrid system, the multilayer positioning is achieved by use of one dimensional Anger principle with BGO crystals. The ultimate resolution and counting rate attainable with the system is discussed in reference to the true to random ratio. Present study indicates that the resolution and efficiency that can be achieved in PCT mode are 5-6 mm fwhm with efficiency gain of over a hundred in comparison to the existing NaI(Tl) ring system at UCSD.