Having thought about this and looked at L.Dutch's answer, I may withdraw my original answer (or leave it just for interest).
Instead I will give a political answer.
As mentioned by L.Dutch, the Soviets came up with a ternary system (see below). Because of the limited use of the Russian language throughout the world the Soviets often resented the fact that US scientific papers got more credence - after all English is the Lingua Franca of science. (This is true by the way, not a fiction, I'll look for references).
Suppose the Russians had won a war over the West. It was common in Soviet Russia for science to be heavily politicised (again I'll look for references). Therefore, regardless of the validity of a non-binary system the Russians could have mandated ternary or some other base simply as a form of triumphalism.
Note - I'm chickening out of finding references at the moment. I've found some but they involve delving into Marxist doctrine or buying an expensive book. My personal knowledge of the situation came from talking to a British scientist who was digging through old Russian papers looking for bits that had been missed or had been distorted by doctrine. Maybe I'll delve further but not right now.
The first modern, electronic ternary computer Setun was built in 1958 in the Soviet Union at the Moscow State University by Nikolay Brusentsov