Electronic computing relies on systematically controlling the flow of electrons to perform logical functions. Various technologies and logic families are used in modern computing, each with its own tradeoffs. In particular, diode logic allows for the execution of logic with many fewer devices than complementary metal-oxide-semiconductor (CMOS) architectures, which implies the potential to be faster, cheaper, and dissipate less power. It has heretofore been impossible to fully utilize diode logic, however, as standard diodes lack the capability of performing signal inversion. Here we create a binary logic family based on high and low current states in which the InMnAs magnetoresistive semiconductor heterojunction diodes implement the first complete logic family based solely on diodes. The diodes are used as switches by manipulating the magnetoresistance with control currents that generate magnetic fields through the junction. With 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. These circuits are evaluated based on InMnAs experimental data, and design techniques are discussed. As Si scaling reaches its inherent limits, this spin-diode logic family is an intriguing potential replacement for CMOS technology due to its material characteristics and compact circuits.