I think you've confused the representation with the computation. Sure maybe that binary number could represent a universe state in some encoding. But there's no computation happening to it. It's static.
>I believe that mathematics is a mental construct, mathematics does not exist without brains
Brains evolved through natural selection to survive in the universe we exist in. Ideas similarly "evolved" to be good at modelling the universe. If mathematics didn't exist outside of our head, it would be useless. If there are two apples on the ground, and two more fall of a tree, then there are four apples on the ground. This is true whether or not a human is there to observe it and count them.
>I believe that mathematics is a mental construct, mathematics does not exist without brains
Brains evolved through natural selection to survive in the universe we exist in. Ideas similarly "evolved" to be good at modelling the universe. If mathematics didn't exist outside of our head, it would be useless. If there are two apples on the ground, and two more fall of a tree, then there are four apples on the ground. This is true whether or not a human is there to observe it and count them.