  A general relativistic, stationary and axisymmetric black hole in a
four-dimensional asymptotically-flat spacetime is fully determined by its mass,
angular momentum and electric charge. The expectation that astrophysically
relevant black holes do not posses charge has resulted in a limited number of
investigations of moving and charged black holes in the dynamical, strong-field
gravitational (and electromagnetic) regime, where numerical studies are
necessary. Apart from having a theoretical interest, the advent of
multimessenger astronomy with gravitational waves offers new ways to think
about charged black holes. In this work, we initiate an exploration of charged
binary black holes by generating valid initial data for general relativistic
simulations of black hole systems that have generic electric charge, linear and
angular momenta. We develop our initial data formalism within the framework of
the conformal transverse-traceless (Bowen-York) technique using the puncture
approach, and apply the theory of isolated horizons to attribute physical
parameters (mass, charge and angular momentum) to each hole. We implemented our
formalism in the case of a binary system by modifying the publicly available
TwoPunctures and QuasiLocalMeasures codes. We demonstrate that our code can
recover existing solutions and that it has excellent self-convergence
properties for a generic configuration of two black holes.
