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Functional decomposition has recently been adopted for look-up table (LUT)-based field-programmable gate array (FPGA) technology mapping with good results. In this paper we propose a novel method to unify functional single-output and multiple-output decomposition. We first address a compatible class encoding algorithm to minimize the number of compatible classes in the image function. After applying the encoding algorithm, we can therefore improve the decomposability in the subsequent decomposition of the image function. The above encoding algorithm is then extended to encode multiple-output functions through the construction of a hyperfunction. Common subexpressions among these multiple-output functions can be extracted during the decomposition of the hyperfunction. Consequently, we can handle multiple-output decomposition in the same manner as single-output decomposition. Experimental results show that our algorithms are promising.