Logical systems are the core essence of our current computation system and these logics are based on binary number system. For the last few decades binary has been used as a core system. But in the upcoming future, it would require more efficient performance, high rate of computation and strong base in machine control system and artificial intelligence. So, the upgrade of computer number system is very necessary for more scope, speed, computation and analysis. The next step to move from binary is ternary (more precisely balanced ternary) and it is already used to develop a system several times. The implementable ternary number system in computer is the balanced ternary number system which was previously used to develop “SETUN”. Actually, the balanced ternary number system is the binary implemented form of ternary using the system of overflow throughout the entire conversion. This is a continuous overflow system and overlaps the value every single time when the remainder is two (2). In order to overlap the value it is necessary to check if the remainder is 2 or not; this check increases the number of logical condition used during the conversion. Thus continuous overflow generally implies in complexity due to checking more logical conditions resulting in less efficient system performance. Considering this as a key point, the combined balanced ternary number system is developed which works with this overflow technique in order to increase the system performance. In the combined balanced ternary number system, the continuous remainder testing and overflow technique is replaced by partial overflow technique. In the partial overflow technique the overflow during conversion for any specific value is prohibited. In this number system overflow value is introduced with the remainder rather than the convertible value which results in less number of condition checking during the entire conversion process. As less logical condition is used, this new number system sharpens the performance of the conversion.