Centrala begrepp
A comprehensive algebraic framework tailored to asymmetric logic functions, such as inverted-input AND (IAND) and implication, to enable efficient synthesis and minimization of logic circuits for emerging computing technologies.
Sammanfattning
This paper presents a complete Boolean algebraic framework specifically designed for asymmetric logic functions, which are prevalent in emerging computing devices like memristors and spintronic devices. The framework introduces fundamental identities, theorems, and canonical normal forms that lay the groundwork for efficient synthesis and minimization of such logic circuits without relying on conventional Boolean algebra.
The key highlights are:
- Algebraic identities and laws for IAND and IMPLY operations, including interaction with high/low logic, idempotency, commutation, associativity, distributivity, and De Morgan's law.
- Canonical normal forms for asymmetric logic, including Sum of IANDs (SOI), NAND of Implications (NOI), IAND of Sums (IOS), and IMPLY of NANDs (ION).
- Establishment of a logical relationship between IAND and IMPLY operations, showing that they are "De Morgan duals" of each other.
- Demonstration of how this algebraic framework can enable significant computational advantages, as exemplified by a 28% reduction in computational steps for a memristive full adder circuit compared to previous manual optimization approaches.
The proposed algebraic framework lays the foundation for much greater future improvements in logic design automation for emerging computing technologies that leverage asymmetric logic functions.
Statistik
The memristive full adder circuit designed using the proposed minimization algorithm achieved a 28% reduction in the number of computational steps compared to the best manually-optimized full adder.
Citat
"The increasing advancement of emerging device technologies that provide alternative basis logic sets necessitates the exploration of innovative logic design automation methodologies."
"Existing logic design techniques inadequately leverage the unique characteristics of asymmetric logic functions resulting in insufficiently optimized logic circuits."
"The presently-proposed algebraic framework lays the foundation for much greater future improvements."