Arithmetic Operators Based on the BSCB representation
نویسندگان
چکیده
We introduce implementations of arithmetic operators based on the binary stored-carry-or-borrow (BSCB) representation. Several BSCB arithmetic elements, including full-adder, ripple-carry adder, and carry-lookahead adder are presented, followed by detailed design of an array multiplier. In the latter design, the conventional initial AND matrix is transformed and expressed with a redundant radix-2 representation. Each line of the resulting matrix is processed by an accumulation operator with the BSCB representation. Due to a specific property of the multiplication process, this operator is simpler than a standard full-adder cell in terms of gate count, while maintaining the same propagation latency. The entire multiplier is implemented with only XOR and AND gates, thus improving its testability and reliability.
منابع مشابه
Arithmetic Aggregation Operators for Interval-valued Intuitionistic Linguistic Variables and Application to Multi-attribute Group Decision Making
The intuitionistic linguistic set (ILS) is an extension of linguisitc variable. To overcome the drawback of using single real number to represent membership degree and non-membership degree for ILS, the concept of interval-valued intuitionistic linguistic set (IVILS) is introduced through representing the membership degree and non-membership degree with intervals for ILS in this paper. The oper...
متن کاملARITHMETIC-BASED FUZZY CONTROL
Fuzzy control is one of the most important parts of fuzzy theory for which several approaches exist. Mamdani uses $alpha$-cuts and builds the union of the membership functions which is called the aggregated consequence function. The resulting function is the starting point of the defuzzification process. In this article, we define a more natural way to calculate the aggregated consequence funct...
متن کاملHesitant Fuzzy Linguistic Arithmetic Aggregation Operators in Multiple Attribute Decision Making
In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic and geometric aggregation operators with hesitant fuzzy linguistic information. Then, motivated by the idea of traditional arithmetic operation, we have developed some aggregation operators for aggregating hesitant fuzzy linguistic information: hesitant fuzzy linguistic weighted average (...
متن کاملError bounds in approximating n-time differentiable functions of self-adjoint operators in Hilbert spaces via a Taylor's type expansion
On utilizing the spectral representation of selfadjoint operators in Hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in Hilbert Spaces via a Taylor's type expansion are given.
متن کاملA parametric representation of fuzzy numbers and their arithmetic operators
Direct implementation of extended arithmetic operators on fuzzy numbers is computationally complex. Implementation of the extension principle is equivalent to solving a nonlinear programming problem. To overcome this difficulty many applications limit the membership functions to certain shapes, usually either triangular fuzzy numbers (TFN) or trapezoidal fuzzy numbers (TrFN). Then calculation o...
متن کامل