Results 301 to 310 of about 12,102,780 (375)

FROM THE HISTORY OF THE BINARY NUMBER SYSTEM. THOMAS HARRIOT

, 2020
For the first time in the Russian-language literature, the article analyzes the works of the English mathematician, geographer and astronomer Thomas Harriot (1560–1621) related to the binary number system.
D. Zlatopolski, V. Shilov
semanticscholar   +1 more source

XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks

European Conference on Computer Vision, 2016
We propose two efficient approximations to standard convolutional neural networks: Binary-Weight-Networks and XNOR-Networks. In Binary-Weight-Networks, the filters are approximated with binary values resulting in 32\(\times \) memory saving.
Mohammad Rastegari, Vicente Ordonez, Joseph Redmon, Ali Farhadi   +3 more
semanticscholar   +1 more source

On the Addition of Binary Numbers

IEEE Transactions on Computers, 1970
An upper bound is derived for the time required to add numbers modulo 2n, using circuit elements with a limited fan-in and unit delay, and assuming that all numbers have the usual binary encoding. The upper bound is within a factor (1 + e) of Winograd's lower bound (which holds for all encodings), where e→0 as n→∞, and only O(n log n) circuit elements ...
openaire   +3 more sources

On representation of numbers by binary forms

Mathematical Notes of the Academy of Sciences of the USSR, 1968
An effective method is given for finding all rational points, the denominators of which are formed from a finite number of fixed primes, on the curvef (x, y)=A, wheref (x, y) is a binary form of degree three at least, irreducible over the field of rational numbers, and A is a rational number.
A. I. Vinogradov, A. I. Vinogradov, V. G. Sprindzhuk, V. G. Sprindzhuk   +3 more
openaire   +3 more sources

Optical on-the-fly conversion of a modified signed digit into two's complement binary number representation.

Optics Letters, 1988
An optical carry-free technique is introduced for conversion of a modified signed digit (MSD) into two's complement binary number. Using a combination of optical polarizing beam splitters and retardation waveplates, the proposed device performs this ...
Y. Li, J. Zhu, G. Eichmann
semanticscholar   +1 more source

Binary Numbers and Arithmetic

1981
A wide range of numbering systems is in use today, the most common being the decimal or denary system. This system utilises the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. It is important to note that the first number is zero, and that the tenth number is nine.
openaire   +2 more sources

The Number of Gaps in Binary Pictures

2005
This paper identifies the total number of gaps of object pixels in a binary picture, which solves an open problem in 2D digital geometry (or combinatorial topology of binary pictures). We obtain a formula for the total number of gaps as a function of the number of object pixels (grid squares), vertices (corners of grid squares), holes, connected ...
BRIMKOV V. E, MAIMONE, ANGELO, NORDO, Giorgio, BARNEVA R. P, KLETTE R.   +4 more
openaire   +3 more sources

On the Number of Classes of Binary Matrices

IEEE Transactions on Computers, 1973
Cellular switching theory gives rise to the problems of counting the number of equivalence classes of m X n matrices of zeros and ones under: 1) row and column permutations; and 2) row and column permutations together with column complementations. A number of techniques are given for the solution of these problems.
openaire   +3 more sources

Binary numbers in Indian antiquity

Journal of Indian Philosophy, 1993
It is shown that binary numbers were first discovered as early as the second or third century A.D. by Piṅgala, in his \textit{Chandaḥśāstra} (which was translated and edited by A. Weber in 1863), in an attempt to classify Sanskrit verse meters. The fact that in Piṅgala's binary system the low digit is on the left and the high value on the right ...
openaire   +2 more sources

Piṅgala Binary Numbers

2009
Besides using several mathematical formulas regarding permutations, combinations, geometric progression, and binomial coefficients, Ācārya Piṅgala applied binary codes to discuss the listing of even meters. Piṅgala’s Chandas Śāstram, the science of meters is the oldest authoritative work on Vedic and Sanskrit prosody.
openaire   +2 more sources