how to design an electronic circuit that convert a binary sequence to Manchester code
The result of Manchester encoding means that you can feed the modified signal through a high pass filter and get equal positive and negative values. The nature of using an exor gate means that you have removed any important dc information in the signal hence, just add a high pass filter to remove that dc offset. 



As you can see from above, standard data (NRZ) contains spectral content at DC whereas Manchester encoding (the solid black line) contains no dc spectral component. Basically an exor gate is a phase shift modulator.

If you need a bigger signal, amplify it.