Quantum-effect devices utilizing resonant tunneling are promising candidates for future nano-scale integration. Originating from the technological progress of semiconductor technology, circuit architectures with reduced complexity are investigated by exploiting the negative-differential resistance of resonant tunneling devices. In this paper a resonant tunneling device threshold logic family based on the Monostable-Bistable Transition Logic Element (MOBILE) is proposed and applied to different parallel adder designs, such as ripple carry and binary carry lookahead adders. The basic device is a resonant tunneling transistor (RTT) composed of a resonant tunneling diode monolithically integrated on the drain contact layer of a heterostructure field effect transistor. On the circuit level the key components are a programmable NAND/NOR logic gate, threshold logic gates, and parallel counters. The special properties of MOBILE logic Sates are considered by a bit-level pipelined circuit style. Experimental results are presented for the NAND/NOR logic gate.