ABSTRACT: Even though real world analysis is non-linear and uncertain, most of the power system network analyses are the approximation rather than the worst case results. One of the power system network analysis mechanisms which is based on deterministic input is a load flow analysis. Due to the penetration of renewable energy sources and the environmental temperature change, power system network inputs are no longer constant rather varies between upper and lower extremes constantly. The main load flow analysis constants considered to vary with the variation of input are the active and reactive power at the generator and the buses. In order to get a load flow solution for the varying input power a probabilistic load flow analysis based on complex affine arithmetic (CAA) is proposed and tested on standard IEEE 57 bus systems. The result is validated by its mid way conservation of the deterministic load flow analysis result and a probabilistic Monte Carlo approach.
While the field of error analysis is well studied the application of error analysis has been limited thus far, with applications generally being found in high level industrial and scientific fields and in safety critical software. One of the primary reasons for this limited implementation is that error analysis techniques tend to be highly complex and understanding of error analysis theory tends to be limited to specialists in the fields of computer architecture, computer arithmetic and numerical analysis. Dynamic error analysis techniques can require significant changes to existing source code and due to the requirement for extended precision or changes to memory structures these systems are often implemented in software rather than hardware impacting performance. Static analysis techniques are also difficult to implement due to their requirement for in depth understanding of the mathematical models involved, and do not scale well beyond small sub-routines . In order to address these issues we have endeavoured to develop automated methods that simplify the implementation of dynamic error analysis methods and aim to achieve the following:
A bstract – Arithmetic adder is the most important basic element for m any digital applications. In paper different types of ad d e r s a r e t a ken for such as Ripple Carry Adder, Carry Save a d d e r , C a r r y L ook ahead adder, Carry Increment adder, Carry Select adder and C a rry Skip adder. Here in this paper introducing a novel techniq u e f or designing a new Carry Select adder f o r m u l t i p r e c i s i o n a rithmetic circuits. By using this technique improvements has been a c hieved like low latency and less power consumption and a l o n g w ith less gate count. Experim entally synthesized and simulated b y u sing Xilinx ISE14.7, also tested in SPARTAN3E, X C 3 S 1 6 0 0 E w i t h s p e e d o f
The Arithmetic and Logic Unit is one of the key module in digital signal processors. All the digital domain based technology depends on the operations performed by ALU. Therefore there is a need to design an efficient ALU. ALU consists of arithmetic unit and Logical unit. Arithmetic unit is designed using multiplier adder etc. The multiplier in the proposed work is designed using a unique tree structure which has lesser delay. The adder unit used is Knowles adder which is a parallel prefix adder and has lesser delay compared to other known prefix adders. The proposed work is better in terms of delay. A trade off has been made between area and delay in the proposed design. The savings of power for most power effective architectures range from 19.38% to 33.87%. The proposed design is described using Verilog hardware description language. For Synthesis of the design Cadence RTL compiler has been used.
A floating point arithmetic unit designed to perform operations on floating point numbers as well as fixed point numbers. Floating point numbers can support a much wider range of values in comparison to fixed point representation. Floating Point units are mainly used in high speed objects recognition system, high performance computer systems, embedded systems and mobile applications. To represent very small values or very large values, large range is required as the integer representation is no longer appropriate to represent these numbers so these values can be represented by using floating point representation that is based on the IEEE-754 standard. The proposed floating point arithmetic unit is designed using single stage implementation. Due to single stage implementation the complex logic operations which consist of various multiple numbers of stages are converted into single stage implementation. So by using single stage implementation the time requires to reach data from input to output becomes less. The proposed unit is designed in VHDL, simulated in Questa Sim simulator and implemented on vertex-7 FPGA.
floating point arithmetic operations on top of a secure multiparty computation engine. The general approach is generic, but in order to obtain the efficient real implementation, platform-specific design decisions have been made. In the current paper, we based our decisions on the architecture of Sharemind which served as a basic platform for our benchmarks. We also showed how to implement several elementary functions and benchmarked their performance. However, by replacing the specific optimisations with generic algorithms or other specific op- timisations, these floating point algorithms can be ported to other secure com- putation systems. We concluded by implementing the algorithm for computing the probability of satellite collision and benchmarked the performance of this implementation.
Keywords- Arithmetic Logical Unit, CSLA, RCA, Power, Area
I. I NTRODUCTION
Design of area- and power-efficient high- speed data path logic systems are one of the most substantial areas of research in VLSI system design. An arithmetic processor comprising: an arithmetic logic unit having a plurality of arithmetic circuits each for performing a group of associated arithmetic operations, such as finite field operations, or modular integer operations. The arithmetic logic unit has an operand input data bus, for receiving operand data there on and a result data output bus for returning the results of the arithmetic operations there on. A register file is coupled to the operand data bus and the result data bus. The register file is shared by the plurality of arithmetic circuits. Further a controller is coupled to the ALU and the register file, the controller selecting one of the plurality of arithmetic circuits in response to a mode control signal requesting an arithmetic operation and for controlling data access between the register file and the ALU and whereby the register file is shared by the arithmetic circuits.
This course will be interested in the description, in analytic terms, of various spaces of functions on Γ \G where G is the group of real points on a reductive group defined over Q, and Γ is an arithmetic subgroup.
What do I mean by ‘analytic terms’? Well, the ultimate goal in the theory of automorphic forms is to derive applications to number theory, particularly those relating to a wide range of L-functions. There are many applications of this kind that depend ultimately on sophisticated analysis, and indeed can often be formulated only given a number of results in analysis. I shall occasionally mention these, but for the most part I shall not say much about them, even when the topic at hand is relevant. You can already discern my bias if you compare my account with most others in the recent literature, which are largely concerned not with arithmetic quotients Γ \G but with adelic quotients G(Q)\G(A), where G(Q) is the Q-rational group implicitly determining Γ, and A is the ring of rational adeles.
This course will be interested in the description of various spaces of functions on Γ\G, in analytic terms, where G is the group of real points on a reductive group defined over Q, and Γ is an arithmetic subgroup.
What do I mean by ‘analytic terms’? Well, the ultimate goal in this business is to derive applications to number theory, and there are many such applications that depend ultimately on analysis, and indeed can often be formulated only given a number of results in analysis. I shall occasionally mention these, but for the most part I shall not say much about them. You can already discern my bias if you compare my account with most others in the recent literature, which are largely concerned not with arithemetic quotients Γ\G but with adelic quotients G(Q)\G(A), where G(Q) is the Q-rational group implicitly determining Γ, and A is the ring of rational adeles. This is no loss for me, since all the hard analysis on adelic quotients reduces ultimately to hard analysis on arithmetic quotients. Restricting to arithmetic quotients should make the basic points of analysis clearer. In compensation, the analysis can be fairly interesting.
 N. Srinivasa Rao and B.Vijaysree, “Design the 2*1 MUX with 2T Logic and Comparing the Power Dissipation and Area with Different logics”, IJAREEIE, Vol. 4 Issue 3, March 2015.
 Maroju SaiKumar and Dr.P.Samundiswary,
“Design and Performance Analysis of Various Adders using Verilog”, IJCSMC, Vol.2 Issue 9, September 2013.
investigation to a mapping procedure that views the input integers as a set of conflicting answers to a binary question, and attempt to figure out the single integer that best reflects the combined “wisdom” of the input answers. Thereby we construct the proposed
arithmetic as ground tool for discriminant analysis. On the other end, the many-to-one mapping suggests this arithmetic as a fundamental hashing function, and the complexity of data loss suggests a new primitive for asymmetric cryptography. This arithmetic evolved from practical algorithms used by the author in his engineering practice, where the
Commercial FPGA components are optimised for a wide range of applications, as they are intended for universal use. Significant research has been conducted in the optimisation of these universal FPGAs, using benchmark circuits from dif- ferent application domains (e.g. Betz et al., 1999). An analy- sis of the logic- and interconnect requirements of arithmetic- datapaths reveals that the architectural requirements differ significantly from irregular logic. In this contribution, an eFPGA-architecture and the corresponding structural ele- ments have been tailored to an arithmetic-oriented applica- tion domain. Considering the interconnect requirements of different applications mapped to FPGAs, it is useful to con- sider the histogram of the lengths of allocated interconnec- tions. Fig. 4 shows such a qualitative histogram of the al- located connections between logic elements. For irregular logic, the number of connections between the LEs decreases with the connection length L. Arithmetic-datapaths, however, have a very high locality, hence exposing a peak in the distri- bution for short connections. Only few lines of intermediate length are required, while some long connections, usually representing broadcast lines, are used.
V. C ONCLUSION
The datapath is often represented by a polynomial so exploring its range is helpful from both correctness and the performance point of view. Range analysis relies on simulation or static methods, but they both have weakness of low efficiency and loose bounds. In this paper, we describe the efficient static analysis to handle polynomials, and design a new algorithm to compute the range bounds by the efficient AT polynomial search. The method does not rely on simulation and handles efficiently for large arithmetic circuits. The output bit-widths are allocated by the range easily and procures smaller bits.
IX. E XPERIMENTAL R ESULTS
This section presents four experiments to verify the above analysis from different aspects. We use the first experiment to verify the correctness of (37), the refined formula for ψ n,R (n). Then some examples of the HDS of tailed DAC are given. Next, we show how ψ n,R (d) for small d varies w.r.t. tail length t. Finally, some examples are given to illustrate how the ACC and rate loss of tailed DA codes varies w.r.t. tail length t.
Emerging economies which have adopted inflation targeting and which combine low credibility, high public debt, and a high interest rate suffer from a typical problem. Increases in the interest rate to reduce departures of inflation from the target imply higher primary surplus for stabilizing public debt/GDP ratio. This tricky situation is known as “unpleasant fiscal arithmetic” (UFA). This article develops a theoretical model showing how an increase in financial openness and capital account liberalization can mitigate UFA. Furthermore, empirical evidence from the Brazilian case through OLS, GMM, and GMM system methods is offered. The findings denote that increases in capital mobility and financial openness work as a commitment technology which contribute to the success of the inflation targeting and thus reduce the risk of UFA occurs.
Cílem této diplomové práce je implementace algoritmů navržených Prof. Dr. Markusem Müller-Olmem a Prof. Dr. Helmutem Seidlem v odborném článku Analysis of Modular Arithmetic. Tyto algoritmy byly implementovány jako součást aplikace, která zpracovává program, načtený na vstupu této aplikace. Načtený program musí být napsán v jednoduchém programovacím jazyce, který byl navržen speciálně pro potřeby této práce. Tento jazyk pracuje pouze s globálními proměnnými celočíselného typu. Umožňuje však použití neomezeného množství funkcí, které se mohou navzájem rekurzivně volat. Hlavním úkolem implementované aplikace je vypočtení lineárních vztahů mezi hodnotami proměnných pro každé místo v kódu načteného programu. Vypočtené lineární vztahy platí v modulární aritmetice, kde se veškeré operace provádějí v modulo 2 , kde je počet bitů. Stanovení rozsahu, v jakém mají výpočty probíhat (tedy stanovení počtu bitů), se provádí parametrem při spouštění aplikace. Výstupem aplikace je nový soubor obsahující původní program doplněný o výpis platných lineárních vztahů za každým příkazem v programu.
8 Peano Arithmetic
In this final section of the project we will summarize the postulates Peano developed for axiomatic treatment of arithmetic, and will also give a modern analysis of his postulates.
As we saw, in order to express Peano’s five postulates, our first-order language needs to have the successor function s and the constant 0. Also, the formal treatment of addition and multiplication requires that we expand our first-order language with two binary functions + and ×, and add to Peano’s five postulates four more postulates, two of which govern the behavior of addition and the other two that of multiplication. The resulted system is known as Peano Arithmetic and is denoted PA. In PA we can develop arithmetic on a purely formal basis. In particular, all the basic properties of addition and multiplication, such as associativity, commutativity, and distributivity of multiplication over addition become theorems of PA. We can also define subtraction, division, and < in PA and prove their basic properties.
I work on questions in geometric group theory by making use of topological methods to better understand finitely generated groups. Arithmetic groups form a particularly rich family of groups that are examples of latices in Lie groups. The theory of arithmetic groups draws from many fields including geometry, number theory, and group theory. Arithmetic groups share common qualities with many other families of groups, Kac- Moody groups, tree lattices, Aut(F n ), MCG, CAT(0)-groups and others.