As we know, base $12$ is far superior to base $10$, but only outdone by base $2$. $N_b$ denotes a number $N$ is base $b$. This is done by $$N_b=\sum_{n=-\infty}^\infty a_nb^n$$$$0\le a_n\le b,a_n\in\mathcal{Z}$$ But what if I said there was a more complicated way to express numbers and you use it every day? I'll only go into integers, since that's all I've worked out, but you'll understand what I mean. Time.$$T(\operatorname{seconds})=a_1\cdot60+a_2\cdot60\cdot60+a_3\cdot24\cdot60\cdot60+a_4\cdot7\cdot24\cdot60\cdot60$$Or more generally. $$N_{(b_0,\phantom.b_1,\phantom. b_2,\phantom.\cdots)}=\sum_{n=0}^\infty a_n\prod_{m=0}^nb_m$$ So This would mean that not every place can hold the same digit. So you might have the number $N_{(4,5,6,7)}=543$ and $N+1=1000$ Where $b_0$ would be $4$ and represent the $3$'s place.
Also just a side note, base $1$ is interesting because $1000_1=.000001_1$