  We present simple yet extremely accurate coupled-wave models describing the
formation of bound states in the continuum (BICs) in 1D-periodic guided-mode
resonant gratings (GMRGs) consisting of a slab waveguide layer with a binary
grating attached to one or both of its interfaces. Using these models, we
obtain simple closed-form expressions predicting the locations of the BICs and
quasi-BICs in the $\omega$-$k_x$ parameter space. We study two mechanisms of
the BIC formation: coupling between two counter-propagating guided modes and
coupling between a guided mode and a Fabry-P\'erot mode. The BIC conditions for
the two considered mechanisms are formulated in terms of the scattering
coefficients of the binary grating. The predictions of the presented models are
in excellent agreement with the results of rigorous numerical simulations
obtained using the Fourier modal method.
