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While most modern computing technologies utilize Si complementary metal-oxide-semiconductor (CMOS) transistors and the accompanying CMOS logic family, alternative devices and logic families exhibit significant performance advantages. Though heretofore impractical, diode logic allows for the execution of logic circuits that are faster, smaller, and dissipate less power than conventional architectures. In this paper, magnetoresistive semiconductor heterojunctions are used to produce the first complete logic family based solely on diodes. We utilize the diode magnetoresistance states to create a binary logic family based on high and low currents in which a full range of logic functions is executed. The diode is used as a switch by manipulating its magnetoresistance with current-carrying wires that generate magnetic fields. Using this device structure, we present basis logic elements and complex circuits consisting of as few as 10% of the devices required in their conventional CMOS counterparts. This diode logic family is therefore an intriguing potential replacement for CMOS technology as Si scaling reaches its inherent limits.