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In this paper, we present a novel circuit design approach for radiation hardened digital electronics. Our approach is based on the use of shadow gates, whose task it is to protect the primary gate in case it is struck by a heavy cosmic ion. We locally duplicate the gate to be protected, and connect a pair of diode-connected transistors (or diodes) between the outputs of the original and shadow gates. These transistors turn on when the voltages of the two gates deviate during a radiation strike. Our experiments show that at the level of a single gate, our circuit structure has a delay overhead about 1.76% on average, and an area overhead of 277%. At the circuit level, however, we do not need to protect all gates. We present a methodology to selectively protect specific gates of the circuit in a manner that guarantees radiation tolerance for the entire circuit. With this methodology, we demonstrate that at the circuit level, the average delay overhead is about 3% and the average placed-and-routed area overhead is 28%, compared to an unprotected circuit (for delay mapped designs). We also propose an improved circuit protection algorithm to reduce the area overhead associated with our approach. With this approach for circuit protection, the area and delay overheads are further lowered.