Two-dimensional Gunn devices are suitable for integrating many logic devices on an epitaxial GaAs layer grown on a semi-insulating substrate. In this paper, a planar Gunn device with two separated cathodes is proposed and the fundamental logic operations, such as the exclusive OR, the inclusive OR and the inhibitor functions, are discussed theoretically and experimentally. The domain dynamics in this planar device has been examined by the computer simulation. The regions of the reliable operations are also shown by a diagram. Our experimental results confirmed the above logic operations.