The brilliance of Gauss’s solution is that it bypasses the need for brute force computation. Instead, he had the insight to ‘fold’ the integers provided. Rather than adding the integers in sequence, Gauss paired them together to obtain fifty copies of 101. That gives a final total of 50*101, or 5050. Gauss probed the structures of numbers and arithmetic to reduce the intended scope of the problem to a few simple calculations.
A boy wonder from the 1780s shows us where school maths gets it wrong
Junaid Mubeen

I wonder if Gauss had an insight into binary?