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A new method of analyzing bit error rates (BERs) for SFQ circuits and their outputs at GHz speeds will be presented. This method was used to test four- and six-bit pseudorandom code generators. The code generators were operated in free-run mode, i.e., without a synchronization (Reset) pulse. This enabled us to conduct BER testing to much lower levels than when the code generator is operated in Reset mode. The SFQ circuit output was amplified with a superconducting output latch to give voltage levels suitable for display on a sampling scope. The GHz output data was analyzed by external computer software; this permitted extended tests without user supervision. With the code generators operating in free-run mode, they routinely gave bit error rates (BERs) in the 10/sup -11/ range; the best BER recorded was 1.1*10/sup -13/ (2 errors in /spl sim/2.5 hours) at 2 GHz. We have successfully tested these code generators at frequencies in excess of 3.5 GHz with BERs in the 10/sup -10/ range as well.