Reducing Hardware in LUT-Based Mealy FSMs with Encoded Collections of Outputs

A method is proposed that is focused on reducing the chip area occupied by logic elements creating the circuit of Mealy finite state machines (FSMs). The proposed method is aimed at FSM circuits implemented with internal resources of field-programmable gate arrays (FPGA). The required chip area is estimated by the number of look-up table (LUT) elements in a particular circuit. The method is based on mutual application of two methods of structural decomposition. The first of them is based on dividing the set of outputs and using unitary-maximum encoding of collections of FSM outputs. The second method is based on dividing the set of states by classes of compatible states. The optimization is achieved by replacing the maximum binary state codes by two-part codes proposed in this article. Each two-part state code consists of a code of a class including a particular state and a maximum binary code of this state inside a particular class. The proposed approach leads to three-level LUT-based Mealy FSM circuits. The first logic level generates three types of partial functions: unitary encoded outputs, variables encoding collections of outputs, and input memory functions. Each partial function is represented by a circuit including a single LUT. The LUTs from the second logic level generate final values of these functions. The LUTs from the third level implement outputs using collections of outputs. An example of synthesis applying the proposed method is discussed. The experiments were conducted using standard benchmark FSMs. Their results showed significant improving of the area occupied by an FSM circuit. The LUT count decreased on average by 9.49%. The positive side effect of the proposed method was increasing the value of the maximum operating frequency (on average, by 8.73%). The proposed method is advisable to use if a single-level LUT-based implementation of the FSM circuit is impossible