We have sent several spacecraft on trajectories that will ultimately take them into interstellar space (pioneer 10 and 11, voyager 1 and 2, new horizons). how long will it take these spacecraft to travel as far as the nearest stars?

The closest star to our solar system is the Proxima centauri (divided into Alpha century A and Alpha century B).
It will take 4.367 light years to reach those stars. Which is 4.122 × 10^13kilometres.
Meaning it will be years before those spacecraft reach them.

May consider a group  g=({0,1},+)g=({0,1},+)where  ++  will work as the xor operator like we work in boolean algebra. note here, that ‘00’ and ‘11’ are not the usual 0 and 1 that we work with everyday. the elements are  called  ‘00’ and ‘11’ and  may not mean  zero (nothing) and one (single). ‘00’ is the identity for the given binary operator +, meaning that any element operated with ‘00’ gets us that element itself.  for a set  ss  in  g′g′  having more elements than just  {0,1}{0,1}  the values for  a+b∈sa+b∈s, such that  a∈s,b∈sa∈s,b∈s, have to be first defined, only then can you determine the value of  1+11+1. the answer could possibly have been  22  if oanswer is25,000