  We show that deep sparse ReLU networks with ternary weights and deep ReLU
networks with binary weights can approximate $\beta$-H\"older functions on
$[0,1]^d$. Also, for any interval $[a,b)\subset\mathbb{R}$, continuous
functions on $[0,1]^d$ can be approximated by networks of depth $2$ with binary
activation function $\mathds{1}_{[a,b)}$.
