Yes, yes, I knew that when I was two--good grief.

Unity in the binary system is also expressed with 1. There is no choice here. If you say 101101101 is unity, it's not binary, because "unity" means something, and 101101101 also means something in binary, and the properties of unity and the properties of 101101101 are not the same.

You broke the structure.

Maybe you meant to have an example like this: "420" means marijuana in decimal. But in binary it's not so easy.

That's true, because "marijuana" isn't a mathematical property. We've made a correspondence between a decimal number and a non-mathematical concept or symbol, and those don't necessarily survive if we convert to some other base.