  Approximate computing is emerging as an alternative to accurate computing due
to its potential for realizing digital circuits and systems with low power
dissipation, less critical path delay, and less area occupancy for an
acceptable trade-off in the accuracy of results. In the domain of computer
arithmetic, several approximate adders and multipliers have been designed and
their potential have been showcased versus accurate adders and multipliers for
practical digital signal processing applications. Nevertheless, in the existing
literature, almost all the approximate adders and multipliers reported
correspond to the synchronous design method. In this work, we consider robust
asynchronous i.e. quasi-delay-insensitive realizations of approximate adders by
employing delay-insensitive codes for data representation and processing, and
the 4-phase handshake protocols for data communication. The 4-phase handshake
protocols used are the return-to-zero and the return-to-one protocols.
Specifically, we consider the implementations of 32-bit approximate adders
based on the return-to-zero and return-to-one handshake protocols by adopting
the delay-insensitive dual-rail code for data encoding. We consider a range of
approximations varying from 4-bits to 20-bits for the least significant
positions of the accurate 32-bit asynchronous adder. The asynchronous adders
correspond to early output (i.e. early reset) type, which are based on the
well-known ripple carry adder architecture. The experimental results show that
approximate asynchronous adders achieve reductions in the design metrics such
as latency, cycle time, average power dissipation, and silicon area compared to
the accurate asynchronous adders. Further, the reductions in the design metrics
are greater for the return-to-one protocol compared to the return-to-zero
protocol. The design metrics were estimated using a 32/28nm CMOS technology.
