TL;DR: Barrodale and MacLeod as mentioned in this paper showed that there is a definite preponderance of those with an even number of one digits over those containing an odd number, up to 500,000.
Abstract: shows a definite preponderance of those containing an even number of one digits over those containing an odd number. Indeed L. Moser has conjectured that this strange behavior persists forever and that, up to any point, the "evens" are more numerous than the "odds." Recent numerical studies by I. Barrodale and R. MacLeod bear out this conjecture up to 500,000 and indeed show a definite, though slightly undulatory, increase of the excess of evens over odds. [Up to 500,000 this excess numbers around 17000.] The purpose of this note is to prove Moser's conjecture as well as to verify the trends indicated by the Barrodale-MacLeod study. Let us define then, D(n) =the number of one digits in the binary expansion of n,
TL;DR: In this paper, a Galois field multiplier (10) is used for obtaining a product (D) which is stored in an accumulating register (20), of two elements (B, C) which are stored in shift registers (12, 14).
Abstract: A Galois field multiplier (10) is used for obtaining a product (D), which is stored in an accumulating register (20), of two elements (B, C) which are stored in shift registers (12, 14). The product (D) is represented in normal basis form with each binary digit of the bit vector (the product, D) being determined by a sum of the product of the binary digits (bi, ci) representing the two elements. By grouping like ones of one of ordinary digits in the expression for the binary digit of the product and offsetting the suffixes of the binary digits, it is possible to accumulate grouped terms of each of the binary digits of the product simultaneously.
TL;DR: In this article, a method for encoding a message that includes a first set of binary digits is described. But the method is not suitable for the decoding of a message with multiple binary digits and each binary digit has a first value (0) or a second value (1).
Abstract: A method and apparatus for coding and decoding information are disclosed. The method is for encoding a message that includes a first set of binary digits. Each binary digit has a first value (“0”) or a second value (“1”). The method includes receiving a first set of binary digits, generating a second set of binary digits in response to the first set of binary digits (Y), and selecting the values of binary digits in the second set such that the number of binary digits having the first binary value in the second set is higher than the number of binary digits having the first binary value in the first set.
TL;DR: In this article, the number of digits of the numerator and numerator of a fraction to be displayed on a portable electronic computer for conducting fraction calculations has a display including a first multiple-digit display area for displaying numerator.
Abstract: A portable electronic computer for conducting fraction calculations has a display including a first multiple-digit display area for displaying the numerator of a fraction, and a second multiple-digit display area for displaying the denominator of the fraction. The numbers of digits of the numerator and denominator of a fraction to be displayed are obtained. The number of digits of the numerator is compared with the number of digits of the denominator. The difference between the number of digits of the numerator and the number of digits of the denominator is calculated. When the number of digits of the numerator is smaller than the number of digits of the denominator, the numerator is displayed on the first display area with its position shifted to an upper digit place according to the difference. When the number of digits of the denominator is smaller than the number of digits of the numerator, the denominator is displayed on the second display area with its position shifted to an upper digit place according to the difference.
TL;DR: In this paper, a gold finger positioning method and device and a computer readable storage medium are presented. The method comprises the steps that a gold fingerprint image is collected, and the collected gold finger image is subjected to small region delimitation, binarization processing, positioning calculation and comparative analysis.
Abstract: The invention discloses a gold finger positioning method and device and a computer readable storage medium The method comprises the steps that a gold finger image is collected, and the collected gold finger image is subjected to small region delimitation, binarization processing, positioning calculation and comparative analysis, wherein during small region delimitation, a small region with a predetermined size and a predetermined position is judged and delimited according to an obtained contrastive analysis result of all regions except the small region in the gold finger image; during binarization processing, the small region is subjected to binary segmentation to obtain a gold finger binary image of the small region; during positioning calculation, the gold finger binary image of the small region is subjected to positioning calculation to obtain gold finger position data of the small region; during comparative analysis, the gold finger position data of the small region is compared with gold finger predetermined data and obtained gold finger position data of the regions except the small region to obtain a matching result or a non-matching result; and the steps are circulated till all acquired gold finger position data is sufficient for positioning a gold finger, and then positioning is completed Through the gold finger positioning method and device, the gold finger can be positioned efficiently and accurately, and abnormal data can be eliminated