Abstract: Structural representation and technology mapping of
a Boolean function is an important problem in the design of nonregenerative
digital logic circuits (also called combinational logic
circuits). Library aware function manipulation offers a solution to
this problem. Compact multi-level representation of binary networks,
based on simple circuit structures, such as AND-Inverter Graphs
(AIG) [1] [5], NAND Graphs, OR-Inverter Graphs (OIG), AND-OR
Graphs (AOG), AND-OR-Inverter Graphs (AOIG), AND-XORInverter
Graphs, Reduced Boolean Circuits [8] does exist in
literature. In this work, we discuss a novel and efficient graph
realization for combinational logic circuits, represented using a
NAND-NOR-Inverter Graph (NNIG), which is composed of only
two-input NAND (NAND2), NOR (NOR2) and inverter (INV) cells.
The networks are constructed on the basis of irredundant disjunctive
and conjunctive normal forms, after factoring, comprising terms with
minimum support. Construction of a NNIG for a non-regenerative
function in normal form would be straightforward, whereas for the
complementary phase, it would be developed by considering a virtual
instance of the function. However, the choice of best NNIG for a
given function would be based upon literal count, cell count and
DAG node count of the implementation at the technology
independent stage. In case of a tie, the final decision would be made
after extracting the physical design parameters.
We have considered AIG representation for reduced disjunctive
normal form and the best of OIG/AOG/AOIG for the minimized
conjunctive normal forms. This is necessitated due to the nature of
certain functions, such as Achilles- heel functions. NNIGs are found
to exhibit 3.97% lesser node count compared to AIGs and
OIG/AOG/AOIGs; consume 23.74% and 10.79% lesser library cells
than AIGs and OIG/AOG/AOIGs for the various samples considered.
We compare the power efficiency and delay improvement achieved
by optimal NNIGs over minimal AIGs and OIG/AOG/AOIGs for
various case studies. In comparison with functionally equivalent,
irredundant and compact AIGs, NNIGs report mean savings in power
and delay of 43.71% and 25.85% respectively, after technology
mapping with a 0.35 micron TSMC CMOS process. For a
comparison with OIG/AOG/AOIGs, NNIGs demonstrate average
savings in power and delay by 47.51% and 24.83%. With respect to
device count needed for implementation with static CMOS logic
style, NNIGs utilize 37.85% and 33.95% lesser transistors than their
AIG and OIG/AOG/AOIG counterparts.