No, and neither did my children. However we taught them some simple things when they were younger, mostly party tricks like counting to 1000 on their fingers, along with easy ways to tell if numbers divide by 3 and the like. My youngest read Charles Petzold's CODE in Grade 7. He had a teacher who allowed only reading during free time - no writing, no drawing, no staring into space - and so took a very dense book that would last him a good long time. As a result he learned binary and much more. (He also freaked out his teachers, but I can't let that control our actions.)
I don't think learning other bases or number systems is particularly helpful to later programming, even if you're going to bit-twiddle - a grownup can learn base-2 concepts in less than a day. However Boolean logic is super helpful. My oldest couldn't understand why her critical thinking course in college was all surrounded with "now this part is complicated, so hang on" warnings whenever they got near logic problems. She had no problems with any of it.