A binary $(m,n)$-grid is defined as an array of $m$ rows and $n$ columns formed from $mn$ square ceils each of which is crossed by $a$ diagonal. Two $(m,n)$-grids are said to be equivalent iff they can be transformed one into the other by rigid motion in the space. In this paper the number $N(m,n)$ of non-equivalent $(m,n)$-grids are determined for arbitrary natural numbers $m$ and $n$. The formula of N. Hoffman for $N(1,n)$ appears as a special case of our result.