نشریه مهندسی برق و الکترونیک ایران الکترونیک ایران

Signed digit (SD) number systems provide the possibility of constant-time addition, where inter-digit carry propagation
is eliminated. Such carry-free addition is primarily a three-step process; adding the equally weighted SDs to form the
primary sum digits, decomposing the latter to interim sum digits and transfer digits, which commonly belong to
{–1, 0, 1}, and finally adding the transfers to the corresponding (i.e., with the same weight) interim sum digits. All the
final sum digits are therefore obtained in parallel. The special case of radix-2h maximally redundant SD number systems
is more attractive due to maximum symmetric range (i.e., [–2h+1, 2h–1]) with only one redundancy bit per SD, and the
possibility of more efficient carry-free addition. The previous relevant works use three parallel adders that compute sum
and sum±1, where some speed-up is gained at the cost of more area and power. In this paper, we propose an alternative
nonspeculative addition scheme that uses carry-save encoding for representation of the primary sum and interim sum
digits and computes the transfer digits via a fast combinational logic. The simulation and synthesis of the proposed
adder, based on 0.13 μm CMOS technology, shows advantages in terms of speed, power and area.