Algebraic patterns, protocols, and pseudocode for a Quine–McCluskey minimization in lieu of the prime implicant chart

Abstract

Digital gates are the basic electronic component of digital circuits. These circuits perform best when they are simplified as this directly leads to reducing the number of digital gates to implement a logical function, thereby reducing the circuit cost. To do this, Boolean expressions need to be optimally minimized. Karnaugh (K-map) and the Quine–McCluskey (Q–M) methods are well-known techniques to simplify Boolean techniques. K-map executions become complex for many valued functions. Comparatively, the Q–M method is a computer-based faster approach for logic function-based simplification. However, the Q–M method becomes intolerable for many valued logical functions along with its computational complexity and intensiveness simultaneously increasing. Hence, in this study an algebraic sum (A-sum) and cross-check sum (CCS) is proposed, primarily to aid in computationally efficient pairing of high numbered groups particularly for many valued logical functions and secondly to check the correctness of the paired groups as a manner to review the sanctity of the paired groups. In addition, broadly six postulates are proposed to forego the prime implicant chart in the Q–M method. In this study, the expounding of the prior through examples show that by reducing the number of computations from that which would be typically required of by the conventional Q–M method, the performance of the Q–M method is increased along with the reduction of the possibility of an error and an accurate minimization. The results can be expanded to an n-numbered logic function leading to more hardware efficient circuits. Moreover, the postulate approach is simpler, more efficient with less effort than with the use of the prime implicant tables. The proposed approach is a useful aid for both academics and industrialists where logic, digital and circuit design takes precedence at optimal performance.