  We present a systematic study of the magnetic properties of L1$_0$ binary
alloys FeNi, CoNi, MnAl and MnGa via two different density functional theory
approaches. Our calculations show large magnetocrystalline anisotropies in the
order $1~\text{MJ/m}^3$ or higher for CoNi, MnAl and MnGa while FeNi shows a
somewhat lower value in the range $0.48 - 0.77 ~\text{MJ/m}^3$. Saturation
magnetization values of $1.3~\text{MA/m}$, $1.0~\text{MA/m}$, $0.8~\text{MA/m}$
and $0.9~\text{MA/m}$ are obtained for FeNi, CoNi, MnAl and MnGa respectively.
Curie temperatures are evaluated via Monte Carlo simulations and show
$T_\text{C}=916~\text{K}$ and $T_\text{C}=1130~\text{K}$ for FeNi and CoNi
respectively. For Mn-based compounds Mn-rich off-stoichiometric compositions
are found to be important for the stability of a ferro or ferrimagnetic ground
state with $T_\text{C}$ greater than $600~\text{K}$. The effect of
substitutional disorder is studied and found to decrease both
magnetocrystalline anisotropies and Curie temperatures in FeNi and CoNi.
