Related papers: Adding digit vectors

This paper describes a new accumulate-and-add multiplication algorithm. The method partitions one of the operands and re-combines the results of computations done with each of the partitions. The resulting design turns-out to be both…

We will show that in a space of dimension $m$, any family of $2^{m-1}$ distinct Hadamard vectors (where you can choose x or -x but not both) can be partitioned into Hadamard matrices if and only if $m=2^n$ for some n. We will solve this…

The unprecedented performance achieved by deep convolutional neural networks for image classification is linked primarily to their ability of capturing rich structural features at various layers within networks. Here we design a series of…

Joint degree vectors give the number of edges between vertices of degree $i$ and degree $j$ for $1\le i\le j\le n-1$ in an $n$-vertex graph. We find lower and upper bounds for the maximum number of nonzero elements in a joint degree vector…

Within numerical reasoning, understanding numbers themselves is still a challenge for existing language models. Simple generalisations, such as solving 100+200 instead of 1+2, can substantially affect model performance (Sivakumar and…

In this paper, we investigate three general forms of multiple zeta(-star) values. We use these values to give three new sum formulas for multiple zeta(-star) values with height $\leq 2$ and the evaluation of…

We investigate integer numbers which possess at the same time the properties to be triangulars and squares, that are, numbers $a$ for which do exist integers $m$ and $n$ such that $ a = n^2 = \frac{m \cdot (m+1)}{2} $. In particular, we are…

We provide a new way to represent numerical semigroups by showing that the position of every Ap\'ery set of a numerical semigroup $S$ in the enumeration of the elements of $S$ is unique, and that $S$ can be re-constructed from this…

A finite subset $X$ of the Euclidean space is called an $m$-distance set if the number of distances between two distinct points in $X$ is equal to $m$. An $m$-distance set $X$ is said to be maximal if any vector cannot be added to $X$ while…

For polynomials of degree two which have no zeros, the method of accompanying variables is developed and zeros of associated vector polynomials are determined. Our flexible method uses a wide variety of possible vector-valued vector…

In this paper, we consider some additive properties of integers with restricted digit expansions. Let $b\geq 3$ be an integer and $B_b$ be the set of integers whose base $b$ expansions have only digits $\{0,1\}.$ Let $a,b,c$ be three…

Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than $ 1 $ are derived. An application in coding theory is illustrated by showing that multispace…

We study characteristics which might distinguish two-graphs by introducing different numerical measures on the collection of graphs on $n$ vertices. Two conjectures are stated, one using these numerical measures and the other using the deck…

We examine the fundamental problem of constructing depth-optimum circuits for binary addition. More precisely, as in literature, we consider the following problem: Given auxiliary inputs $t_0, \dotsc, t_{m-1}$, so-called generate and…

We consider the problem of constructing fast and small parallel prefix adders for non-uniform input arrival times. This problem arises whenever the adder is embedded into a more complex circuit, e. g. a multiplier. Most previous results are…

The notions of length of a vector field and cosine of the angle between two vector fields over a differentiable manifold with contravariant and covariant affine connections and metrics are introduced and considered. The change of the length…

Decimal-to-binary conversion is important to modern binary computers. The classical method to solve this problem is based on division operation. In this paper, we investigate a decimal-to-binary conversion method based on addition…

The division between two vectors belonging to the same vector space is obtained by elementary procedures of vector algebra and is defined by a matrix. This representation is obtained for two and three dimensional vector spaces. A new vector…

Extended variants of the recently introduced spread unary coding are described. These schemes, in which the length of the code word is fixed, allow representation of approximately n^2 numbers for n bits, rather than the n numbers of the…

We present efficient circuits for the addition of binary numbers. We assume that we are given arrival times for all input bits and optimize the delay of the circuits, i.e.\ the time when the last output bit is computed. This contains the…