To date, several different types of synthetic genetic switches, including riboregulators, riboswitches, and toehold switches, have been developed to construct AND, OR, NOT, NAND, NOR, and NOT IMPLICATION (NIMP) gates. The logic gate can integrate multiple input signals following a set of algorithms and generate a response only if strictly defined conditions are met. However, there are still some logic gates that have not been implemented but are necessary to build complex genetic circuits. Here, based on the toehold switches and three-way-junction (3WJ) repressors, we designed two novel biological Boolean logic gates of IMPLICATION (IMP) and XOR. Subsequently, the outputs of these two logic gates were characterized by fluorescence analysis, indicating that they can achieve the truth tables of logical gates. Furthermore, the fluorescence intensity under the logical TRUE condition was significantly higher than under the logical FALSE condition, suggesting the high dynamic range of the ON/OFF ratios. Because of the programmability of synthetic RNA switches, the constructed RNA logic gates could serve as elementary units to build a versatile and powerful platform for translational regulation and RNA-based biological computation.