I'm not sure what you mean by binary. If you mean binary as in computer binary data, you can do it using the online converter given below: which would give this: 01000001 01000001 01010101 01000001 01010101 01000111 01010101 01010101 01000001 01000001 01010101 01010101 01000111 01000001 01010101 01010101 01010101 01000001 01010101. If you mean binary as in pyrimidine/purine, you can use a simple Excel formula like =if(or(A1="A",A1="G"),"Pur","Pyr").
In addition to using eight-but bytes as in the Text-to-binary example above, and the 1 bit conversion to Pyrimidine or Purine (0 = Purine, 1 = Pyrimidine) ; you could do a two bit conversion to have each base represented (00 = A, O1 = C, 10 = G and 11 = U).
The order you choose may make a difference. Note that in the ACGT order the bases pair as they would in DNA or RNA duplex 00:11 for A:T pair, 01:10 for C:G pair.