Threshold-arithmetic algebraic system and its application in the design of multiple-valued I2L circuits

Based on the characteristics of current-mode circuits, which can easily realize arithmetic operations, the threshold-arithmetic operation and the nonnegative operation are defined in this paper, and the threshold-arithmetic algebraic system suitable to design current-mode circuits is established. Then, HE map is defined and used as the graphic representation of threshold-arithmetic functions, and the method of converting traditional logic function to threshold-arithmetic function with HE Map is expounded. At last, the design method of multiple-valued I
²
L circuits based on threshold-arithmetic algebraic system and HE map is proposed. The HSPICE simulation results using TSMC 0.18μm technology show that the designed I
²
L circuits have the correct functions. The threshold-arithmetic algebraic system is a new simple and effective method for designing the current-mode circuits.