We fabricated ambipolar field-effect transistors (FETs) from multi-layered triclinic ReSe2, mechanically exfoliated onto a SiO2 layer grown on p-doped Si. In contrast to previous reports on thin layers (~2 to 3 layers), we extract field-effect carrier mobilities in excess of 10^2 cm^2/Vs at room temperature in crystals with nearly ~10 atomic layers. These thicker FETs also show nearly zero threshold gate voltage for conduction and high ON to OFF current ratios when compared to the FETs built from thinner layers. We also demonstrate that it is possible to utilize this ambipolarity to fabricate logical elements or digital synthesizers. For instance, we demonstrate that one can produce simple, gate-voltage tunable phase modulators with the ability to shift the phase of the input signal by either 90^o or nearly 180^o. Given that it is possible to engineer these same elements with improved architectures, for example on h-BN in order to decrease the threshold gate voltage and increase the carrier mobilities, it is possible to improve their characteristics in order to engineer ultra-thin layered logic elements based on ReSe2.