They would presumably be rad-hardened, like most military and spacecraft gear intended for high-rad environments.
RAD hardening deals with bit flipping due to event upsets. RAD hardening uses redundancy and distancing to reduce the likelihood of bit flippinp\g.
Although I have not studied the damage mechanism of EMP in detail, a simple search reveals that it works by generating current or ESD which can damage (permanently) computer equipment.
A nuclear EMP is the abrupt pulse of electromagnetic radiation resulting from a nuclear explosion. The resulting rapidly changing electric fields and magnetic fields may couple with electrical/electronic systems to produce damaging current and voltage surges.Excerpted from Electromagnetic Pulse