An associative memory is a special type of artificial neural network that has the purpose of store input patterns with their corresponding output patterns and efficiently recall a pattern from a noise-distorted version. Presented in this article is a new framework for constructing a binary associative memory model based on two new autoinverse operations called extended XOR/XNOR; these new operations are generated from the XOR/XNOR operations, respectively. Two types of associative memory are generated with this model: the max type (XOR-AM max), which is constructed with the maximum of the extended XOR operation, and the min type (XOR-AM min), which is constructed with the minimum of the extended XNOR operation. The XOR-AM max exhibits tolerance against the presence of patterns distorted by dilative noise, whereas the XOR-AM min exhibits tolerance against the presence of patterns distorted by erosive noise; both types of memory converge in a single step, use the same extended XOR/XNOR operator for learning and recalling phases, operate in heteroassociative and autoassociative modes, and show infinite storage capacity for the autoassociative mode. Finally, computer simulation results are presented for the new memories based on the extended XOR/XNOR (XOR-AM), which have better or equal performance compared to other associative memories. For the experiments with mixed noise, the conditions established by the kernel method proposed by Ritter for Morphological Associative Memories were conserved, and the solution algorithm proposed by Hattori for the construction of the kernel patterns of these memories was modified.