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In the recent past, various methods have been proposed to construct deterministic compressed sensing (CS) matrices. Of interest has been the construction of binary sensing matrices as they are useful for multiplierless and faster dimensionality reduction. In most of these binary constructions, the matrix size depends on primes or their powers. In this study, we propose a composition rule which exploits sparsity and block structure of existing binary CS matrices to construct matrices of general size. We also show that these matrices satisfy optimal theoretical guarantees and have similar density compared to matrices obtained using Kronecker product. Simulation work shows that the synthesized matrices provide comparable results against Gaussian random matrices.