The structure of truncated quadtree for binary image is proposed. The collapse of quadtree is performed until the level of small image block of a given size rather than single pixel. The main structure of a binary image is represented by a relative small number of quadtree nodes, and for the small image blocks with mixed colors, they are represented by their raw image pixels. The combination of quadtree and raw image blocks leads to the higher representation efficiency of the truncated quadtree. The truncated quadtree is traversed in a depthfirst manner, and the quadtree nodes and raw image blocks are respectively encoded in the order of traversal, resulting in the truncatedquadtreebased codes of the binary image. The equivalent forms of binary image logical operations on the codes are presented. The experimental results on realworld images show that, with a proper truncating level setting, the memory cost of the truncatedquadtreebased code is 1/10 to 1/3 of the cost of the raw binary image, and the logical operation time on the code is below 1/5 of that of the pixelbypixel approach. The proposed methods are suitable for applications where the number of logical operation is significantly larger than the number of encoding and decoding.