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In this paper, we design some simple schemes for a variety of searches, each of which may be performed in one complete memory cycle using bit-memory logic primarily. The searches we study include the basic equality search, the threshold searches (both greater than and less than searches), and most importantly, the greatest value and the least value searches. For each kind of search, we present both the algorithm suitable for our needs and the logic circuit of the memory cell required by the algorithm. Based on the basic search schemes, an algorithm for ordered retrieval is developed. A comparison for ordered retrieval schemes is then made between the proposed scheme and the previous algorithms. It is found that this algorithm outperforms all the other algorithms compared, particularly in the resolution of multiple responses. Finally, issues relating to LSI implementation, manufacturing defects, modular expansion, and extension to associative sequential memories are discussed.