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On the Addition of Binary Numbers
IEEE Transactions on Computers, 1970An 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 eā0 as nāā, and only O(n log n) circuit elements ...
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The Number of Gaps in Binary Pictures
2005This 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 ...
Valentin E. Brimkov +4 more
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On the Number of Classes of Binary Matrices
IEEE Transactions on Computers, 1973Cellular 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.
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A polarizer for negative binary numbers
1972 IEEE 2nd Symposium on Computer Arithmetic (ARITH), 1972The logical design of a polarizer for negative binary numbers is described and compared with the two's complementer used for positive binary numbers.
Gururaj S. Rao +2 more
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A ``Binary'' System for Complex Numbers
Journal of the ACM, 1965Computer operations with complex numbers are usually performed by dealing with the real and imaginary parts separately and combining the two as a final operation. It might be an advantage in some problems to treat a complex number as a unit and to carry out all operations in this form.
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Mathematics Teaching in the Middle School, 2018
A cartoon involving binary numbers is coupled with a full-page activity sheet.
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A cartoon involving binary numbers is coupled with a full-page activity sheet.
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A self-timed redundant-binary number to binary number converter for digital arithmetic processors
Proceedings of ICCD '95 International Conference on Computer Design. VLSI in Computers and Processors, 2002This paper presents a self-timed converter circuit which converts an n-digit redundant binary number to an (n+1)-bit binary number. Self-timed refers to the fact that the conversion is problem-dependent and requires variable conversion time to complete the operation.
Chin-Long Wey +2 more
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