A New Theory for Multiple Valued Logic Using Convert-Coded-Collect (CCCi) Space

Abstract

The Multiple-Valued Logic (MVL) is one of the keys to building processors in the future because the use of the MVL in control and uP will reduce the number of instructions that are necessary to solve problems and it increases the parallelism. The MVL will increase the speed of the systems and reduce the required memory size and reduce the connections. This paper proposed a new theory to extend the binary logic as operations in a new space called Convert-Coded-Collect space (CCCi). The CCCi space is a closed space that has i integer values, it is used to convert the input to the output in three phases called the convert phase, coding phase, and collect phase respectively. The CCCispace carries out with any integer number of MVLs that depend on the value of i. This paper will discuss two cases of the CCCi space, the first two values (i=2) that are called CCC2; it will prove that CCC2 is more efficient than the Boolean algebra. The other case for this space is CCC4 which has 4 values MVL. This theory is a useful MVL so it has simple functions with a package of advantages. This paper will discuss an example to design a logic multiplier under Boolean logic, under CCC2 space, and under CCC4space to show the advantages of the new theory.