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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 ...
BRIMKOV V. E +4 more
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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.
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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.
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The Universe of Binary Numbers
2017Our main goal in this chapter is to stimulate reasoning by analogy and to show that the same concept can be viewed from several different perspectives. The material presented here is illustrated with a good number of examples. Some of the sections are very speculative, and may appear chaotic.
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1981
A data encoding scheme involving binary tree encodements is presented and analyzed. A closed-form formula for the number of n-bit legal memory configurations is developed. It is shown that the storage capacity loss due the use of this scheme is not significant for large n.
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A data encoding scheme involving binary tree encodements is presented and analyzed. A closed-form formula for the number of n-bit legal memory configurations is developed. It is shown that the storage capacity loss due the use of this scheme is not significant for large n.
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2018
The binary number system (base 2) is a positional number system which uses two binary digits 0 and 1. The binary system is ideally suited to the digital world of computers, as a binary digit may be implemented by an on-off switch. Digital devices that store information or data on permanent storage media such as disks and CDs or temporary storage media ...
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The binary number system (base 2) is a positional number system which uses two binary digits 0 and 1. The binary system is ideally suited to the digital world of computers, as a binary digit may be implemented by an on-off switch. Digital devices that store information or data on permanent storage media such as disks and CDs or temporary storage media ...
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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.
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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.
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Binary Numbers and Digital Electronics
1989The subject of the previous six chapters can be classified as “analog electronics.” The emphasis was on analog voltages that were obtained from sensors and transducers, on analog voltages that adjust the position of actuators and circuits that modify these voltages. Generally these voltages could vary continuously between −15 and +15 V.
W. F. Stoecker, P. A. Stoecker
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The Binary Adder: A Flow Chart for the Addition of Binary Numbers
The Mathematics Teacher, 1973Flowcharting has proved extremely useful in activities ranging from programmed instruction to computer programming. Flowcharting binary addition offers students a mathematical setting for an excellent initial experience in flow charting.
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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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