Conversion algorithm for MPRM expansion

Abstract

Conversion of the Reed-Muller (RM) expansion between two different polarities is an important step in the synthesis and optimization of RM circuits. By investigating XOR decomposition, a new conversion algorithm is proposed to convert MPRM expansion from one polarity to another. First, the relationship between XOR decomposition and mixed polarity is set up. Second, based on this, the operation relation of term coefficients between the two polarities is derived to realize MPRM expansion conversion. And finally, with the MCNC Benchmark, the results of our algorithm show that it is more suitable for dealing with MPRM expansion with more terms. Compared to the previous tabular technique, the conversion efficiency is improved up to approximately 44.39%.

Verification Method for Area Optimization of Mixed-Polarity Reed-Muller Logic Circuits

“…Area constraint and optimization were performed using the DC algorithm. The areas of the combinational logic circuits were calculated according to Equation (5). Finally, the optimized areas of the combinational logic circuits obtained by the two algorithms were compared to verify the superority of the proposed SADPSO algorithm.…”

“…A DC logic synthesis tool was used to impose restriction conditions such that the available logic gate types must be completely consistent with the MPRM and area constraint needs to be executed strictly. The number of equivalent logic gates was calculated according to the area optimization results of the DC logic synthesis and Equation (5). Finally, the area optimization results of the DC logic synthesis and the SADPSO were compared.…”

“…Moreover, this study focuses on the combinational logic circuit with a Reed-Muller (RM) logic circuit [2,3]. The mixed-polarity RM (MPRM) logic circuit is a standard form of the RM logic circuit [4,5]. Area optimization presents a crucial problem for the MPRM logic circuit [6,7] and is the key step in logic synthesis in RM circuits [8].…”

Cube‐Based Synthesis of ESOPs for Large Functions

“…The comparison results in terms of CPU time in seconds are shown in the column labelled "Time for conversion w/ polarity 0". Obviously, the method based on tabular techniques [15] is not appropriate for large functions due to the excessive memory consumption. Among the 17 experimental circuits, the speed of the proposed method is average about 2000 times faster than that of the previous scheme [14] in 7 circuits, and is average about 50 times in other 7 circuits.…”

“…Recently, many other methods have been proposed to compute canonical forms. For instance, some spectral methods are described by matrix transformation [8,16] , and some tabular techniques are extended to coefficient computation [1,15] . However, the above-mentioned algorithms have a common disadvantage that they may involve the procedure of generating the entire truth table, disjoint cubes or other canonical form coefficients, which results in an increase of procedural steps and processing time and consequently restricts their use in large Boolean functions of a SOP or ESOP.…”