Logical Function Decomposition Method for Synthesis of Digital Logical System Implemented with Programmable Logic Devices (PLD)

Abstract

The paper consists in the use of some logical functions decomposition algorithms with application in the implementation of classical circuits like SSI, MSI and PLD. The decomposition methods use the Boolean matrix calculation. It is calculated the implementation costs emphasizing the most economical solutions. One important aspect of serial decomposition is the task of selecting "best candidate" variables for the G function. Decomposition is essentially a process of substituting two or more input variables with a lesser number of new variables. This substitutes results in the reduction of the number of rows in the truth table. Hence, we look for variables which are most likely to reduce the number of rows in the truth table as a result of decomposition. Let us consider an input variable purposely avoiding all interrelationships among the input variables. The only available parameter to evaluate its activity is the number of "l"s or "O"s that it has in the truth table. If the variable has only "1" s or "0" s, it is the "best candidate" for decomposition, as it is practically redundant.

Research on the Function and Application of Some Classical Combinational Logic Products

“…The function table is divided into two parts: truth and control. For the truth part, the output endY0,Y1,Y2,Y3,Y4,Y5,Y6,Y7 indicates that the output level is low, corresponding to the minimum itemsm0,m1,m2,m3,m4,m5,m6,m7 respectively [10]. There are 8 and expressions composed of three logical variables A2, A1 and A0 at the input end, in which each logical variable only appears once as the original variable or the inverse variable.…”