I think this is the wrong question. Any number, if you define them as a representation of digits, is computable in that sense. What isn't necessary computable is the value of a function taken with a certain input or input range. BB numbers, as large as they can be, are themselves finite and therefore "computable" once you know them, but the mapping from natural numbers to BB numbers is not computable. So the real value of a particular function f evaluated at some number say 100 could be as small as 0, but maybe you just can't compute f(100) and know that it's 0.