Nikolay I. Chernov

Basic concept of linear synthesis of multi-valued digital structures in linear spaces

Non-classical approach to logical synthesis of multi-valued elements (ME) of computer equipment, based on principles of linear algebra, is considered. Ideology and basic principles of ME building, which are non-similar to traditional one are described.

The multifunctional current logical element for digital computing devices, operating on the principles of linear (not boolean) algebra

In the article the task of construction of the multifunctional current logical element (MLE), which realizes the analogues of logical functions of the Boolean main functionally complete system (AND, OR, NOT), and also the comparison operation x₁>x₂ is solved for the first time. The quantum of the current I₀ is an equivalent of the standard logical signal here. The suggested MLE also provides the normalization of the signal levels - the generation of the output current, which is equal to I0, without regard to the spread (up to 0.5I₀) of numerical values of the input current logical variables. The concrete logical function, performed by MLE, is determined by the level of the reference DC current I₁ (I₁=0.5I₀, I₁=I₀, I₁=1.5I₀), which is applied to the low-ohmic current input of MLE.

The linear concept of logical synthesis of digital IP-modules of control and communication systems

This paper describes a nonclassical approach to the logical synthesis and circuitry designing of digital IP-modules for computer facilities, control systems and communication. It is based on changing from Boolean algebra by another algebraic structure to the linear algebra. The process of the logical synthesis and circuitry designing of digital devices is described in the offered algebraic structure. The advantages of the considered architectural and circuitry solutions for the synthesis of double-valued and multi-valued digital nodes of different applications in comparison with the double-valued Boolean algebra are demonstrated.

Basic linear elements of k-Valued digital structures

The nonclassical approach to a logic synthesis of k-valued digital structures is considered. It is based on replacing the classical body of mathematics of the logic synthesis (Boolean algebra) – linear algebra. The features of the circuit implementation of operations of linear algebra necessitate going from the potential signals to the current ones. In particular, the new approach is developed, using linear operations, to give forms to initial linear logic structures, from which any logic elements can be further built. The paper considers the circuitry of the corresponding current logic elements of k-valued logics, realized on the base of classical technologies for practical use in the analog-digital interfaces and sensor systems.

Schematic design of digital IC at the base of linear algebra

Critical analysis of developments tendencies of current microelectronics technologies is carried out. As one of feasible direction for further improvement of LSIs generic quality factor, the use of diverse (in comparison with traditional one) body of mathematics for logic synthesis of digital devices - linear algebra, - is proposed. The engineering, technological and operational advantages of computer aids of given class have been designated. The ideology and basic principles of VLSI digital structures at the base of analog transducers for current signals are described.

The linear logic synthesis of k-valued digital structures in the analogous circuitry basis

The non-classical (linear) approach to the logic synthesis of k-valued elements of computer engineering is considered. The method and fundamental principles of building of the circuitry basis, different from traditional ones, are described. The new circuit solutions of k-valued logical gates are suggested.

The element base of the multivalued threshold logic for the automation and control digital devices

The article considers the problems of construction of digital devices, operating on the principles of multivalued (non-Boolean) threshold logic (MTL). The authors suggest the MTL, realized on the base of the current logical elements “minimum” and “maximum”, which solve the task of the limiting “above” and “below” of the output variable at the set logical level. They describe the MTL elements and their computer simulation results. The advantage of the automation and control devices on the MTL lies in the possibility of their operation in demanding conditions.

Threshold synthesis of digital structures in current-mode logic

The article considers the fundamentals of logical synthesis of digital nodes of electronic computer on base of current realization of threshold logic. The examples of logical and circuit description of combinational and sequential logical elements and the results of their computer simulation are given. It is concluded that the proposed approach to the threshold synthesis of digital structures in current logic is promising.

Logic functions representation and synthesis of k-valued digital circuits in linear algebra

The mathematical basics of the non-classical approach to the logical synthesis of k-valued digital structures based on the replacement of the classic mathematical apparatus of logic synthesis (Boolean algebra) to the proposed mathematical apparatus — linear algebra are considered. The logic synthesis process of two valued and multi-valued digital structures in linear algebra including the formation of bases of a linear space and original representation of the implemented logical function are discussed. Mathematical advantages of the proposed approach, which could be the basis for designing of high-speed digital logic structures for various applications are considered.