For simple digital circuits, conventional method of designing circuits can easily be applied. But for complex digital circuits, the conventional method of designing circuits is not fruitfully applicable because it is time-consuming. On the contrary, Genetic Programming is used mostly for automatic program generation. The modern approach for designing Arithmetic circuits, commonly digital circui...

Infimum-supremum interval arithmetic is widely used because of ease of implementation and narrow results. In this note we show that the overestimation of midpoint-radius interval arithmetic compared to power set operations is uniformly bounded by a factor 1.5 in radius. This is true for the four basic operations as well as for vector and matrix operations, over real and over complex numbers. Mo...

Students have difficulty solving arithmetic word problems containing a relational term that is inconsistent with the required arithmetic operation (e.g., containing the term less, yet requiring addition) rather than consistent. To investigate this consistency effect, students' eye fixations were recorded as they read arithmetic word problems on a computer monitor and stated a solution plan for ...

The paper presents (human-oriented) specification and (penand-paper) verification of the square root function. The function implements Newton method and uses a look-up table for initial approximations. Specification is done in terms of total correctness assertions with use of precise arithmetic and the mathematical square root √ . . ., algorithms are presented in pseudo-code with explicit disti...

A new homogeneous computer architecture developed by FPS combines two fundamental techniques for high-speed computing: parallelism based on the binary n-cube interconnect, and pipelined vector arithmetic. The design makes extensive use of VLSI technology, resulting in a processing node that can be economically replicated. Processor nodes incorporate high-speed communications and control, vector...

We present a simple algorithm for computing the arithmetic weight of an integer with respect to a given radix r ≥ 2. The arithmetic weight of n is the minimum number of nonzero digits in any signed radix-r representation of n. This algorithm leads to a new family of minimal weight signed radix-r representations which can be constructed using a left-to-right on-line algorithm. These representati...

A suite of programs is presented to test how accurately the elementary transcendental functions exp, log, sin, cos and atan have been implemented in a computer’s run-time library. The suite is written in the language C and designed to run on any computer with binary floating-point arithmetic rounded in a reasonable way. The suite makes no appeal to extra-precise arithmetic; the tests use only w...

The concept of geometric-arithmetic indices (GA) was put forward in chemical graph theory very recently. In spite of this, several works have already appeared dealing with these indices. In this paper we present lower and upper bounds on the second geometric-arithmetic index (GA2) and characterize the extremal graphs. Moreover, we establish Nordhaus-Gaddum-type results for GA2.

Polygon intersection (clipping) and difference are among the most fundamental operations in computer graphics. To the uninitiated, these problems appear trivial; in fact, they are extremely difficult to perform reliably by computer. Although the graphics literature already provides algorithms for polygon set operations, they have two significant weaknesses: (1) they may fail because they are sp...