Counting in binary can be a fun classroom activity. In my Mathcraft class, I had students line up, facing the class, with each student representing a digit. From the rest of the class's vantage point, the rightmost student represents 1, the next student is 2, the next student is 4, and so on. Then we count. Students raise their hand to represent a one, and lower it to represent zero. Every time we added 1, the student representing 1 switched their arm position. Everyone else watched the person on their left, and if the person on their left lowered their arm, then they would switch their arm position. It took some practice. I felt it was a good idea, but wasn't sure what to do with it beyond use it as a reference experience in other problems involving binary arithmetic.
I also discuss binary arithmetic with my Art of Computing students. They wrote binary counters that displayed in Processing. Here is an example I wrote:
Attended another great course with i2camp, and they have developed a rich curriculum around the math of computers. They use students sitting and standing to represent counting, so I feel I was on the right track. But they took the ideas much further, so I am looking forward to trying this again.