I shall believe that everyone would know binary. We use the base-10 system, which uses 0,1,2,3,4,5,6,7,8 and 9. However, binary only uses 0 and 1.
Before I get technical, I believe that we would have been used to the binary system if it was created. What you learn depends on your surroundings. If you were taught binary first, we would be more used to it. But, is it actually more convenient?
Of course, it only uses 0 and 1. convenient? Possibly. But it would be long. 566 in base-10 is 1000110110.3 digits became 10! However, as strange as it is for a person used to binary to learn 8 more symbols, it is also strange for us to use such long codes.
Addition of two numbers would be a breeze. Either 0, 1, or 1 to the next number. More than that, it would be a bit strange...
Try 1110111000 +1001010101 +1010010100 +1011011101.
But, they would have figured out some way...
Then, multiplication comes. Its practically addition of some numbers. Either add, or not. Multiplication of 3 or more numbers will be strange, but isn't it already?
1011000 +101100 + 1011 =10011111
I'll take some time to think of other examples, but for now, i'll just keep with this...