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, the Soviets came up with a trinary system. 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 trinary or some other base simply as a form of triumphalism.