It's just not the case that the arithmetical algorithms implemented in circuitry have "nothing to do" with pen and paper algorithms. The core ideas of the algorithms we teach kids to add, subtract, multiply, and divide carry over to different bases. The biggest difference between the algorithms implemented in circuitry and those we execute with pen and paper isn't the base, it's the fact that logical gates can be placed in parallel so there's some additional trickery in exploiting that maximally. But understanding the pen and paper algorithms, in whatever base, is still a good starting point for understanding how computers do arithmetic.