  We investigate the fundamental limits of the unsourced random access over the
binary-input Gaussian channel. By fundamental limits, we mean the minimal
energy per bit required to achieve the target per-user probability of error.
The original method proposed by Y. Polyanskiy (2017) and based on Gallager's
trick does not work well for binary signaling. We utilize Fano's method, which
is based on the choice of the so-called ``good'' region. We apply this method
for the cases of Gaussian and binary codebooks and obtain two achievability
bounds. The first bound is very close to Polyanskiy's bound but does not lead
to any improvement. At the same time, the numerical results show that the bound
for the binary case practically coincides with the bound for the Gaussian
codebook. Thus, we conclude that binary modulation does not lead to performance
degradation, and energy-efficient schemes with binary modulation do exist.
