A hybrid floating-point arithmetic processor includes a scheduler, a hybrid register file, and a hybrid arithmetic operation circuit. The scheduler has an input for receiving floating-point instructions, and an output for providing decoded register numbers in response to the floating-point instructions. The hybrid register file is coupled to the scheduler and contains circuitry for storing a plurality of floating-point numbers each represented by a digital sign bit, a digital exponent, and an analog mantissa. The hybrid register file has an output for providing selected ones of the plurality of floating-point numbers in response to the decoded register numbers. The hybrid arithmetic operation circuit is coupled to the scheduler and to the hybrid register file, for performing a hybrid arithmetic operation between two floating-point numbers selected by the scheduler and providing a hybrid result represented by a result digital sign bit, a result digital exponent, and a result analog mantissa.