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# Google searches on 5/25/2015 "The Definition of digital systems"

This definition of a digital system makes reference to the (undecidable) equality relation between real functions. This is not a problem because it is not necessary for the mathematical objects and predicates to be constructively given. It is enough to be able to formulate the necessary axioms without using disjunctions (which is the case for the usual axioms for equality between functions). FROM COINDUCTIVE PROOFS TO EXACT REAL ARITHMETIC: THEORY AND APPLICATIONS By ULRICH BERGER, Swansea University, Swansea SA2 8PP, Wales, UK, e-mail address: [email protected] Logical Methods in Computer Science Vol. 7 (1:8) 2011, pp. 1 24
www.lmcs-online.org
www.lmcs-online.org Submitted Jun. 11, 2010 Published Mar. 23, 2011

# "The History of Digit"

The digit or finger is an ancient and obsolete non-SI unit of measurement of length. It was originally based on the breadth of a human finger. It was a fundamental unit of length in the Ancient Egyptian, Mesopotamian, Hebrew, Ancient Greek and Roman systems of measurement.
In astronomy a digit is, or was until recently, one twelfth of the diameter of the sun or the moon. This is found in the Moralia of Plutarch, XII:23, but the definition as exactly one twelfth of the diameter may be due to Ptolemy. Sosigenes of Alexandria had observed in the 1st century AD that on a dioptra, a disc with a diameter of 11 or 12 digits (of length) was needed to cover the moon.
The unit was used in Arab or Islamic astronomical works such as those of Ṣadr al‐Sharīʿa al‐Thānī (d.1346/7), where it is called‎ iṣba' , digit or finger.
The astronomical digit was in use in Britain for centuries. Heath, writing in 1760, explains that 12 digits are equal to the diameter in eclipse of the sun, but that 23 may be needed for that of the moon, those over 12 representing the extent to which the Earth's shadow is larger than the Moon. The unit is apparently not in current use, but is found in recent dictionaries.

# The History of numbers, integers, digits

A digit is a a numeric symbol (such as "2" or "5") used in combinations (such as "25") to represent numbers (such as the number 25) in positional numeral systems. The name "digit" comes from the fact that the 10 digits (ancient Latin digiti meaning fingers) of the hands correspond to the 10 symbols of the common base 10 numeral system, i.e. the decimal (ancient Latin adjective decem meaning ten) digits.
In a given numeral system, if the base be an integer, the number of digits required would always equal to the absolute value of the base. For example, the decimal system (base 10) has ten digits (0 through to 9), whereas binary (base 2) has two digits (0 and 1). The first true written positional numeral system is considered to be the Hindu Arabic numeral system. This system was established by the 7th century, but was not yet in its modern form because the use of the digit zero had not yet been widely accepted. Instead of a zero, a space was left in the numeral as a placeholder. The first widely acknowledged use of zero was in 876. Although the original Hindu-Arabic system was very similar to the modern one, even down to the glyphs used to represent digits, the direction of places was reversed, so that place values increased to the right rather than to the left.
The exact age of the Maya numerals is unclear, but it is possible that it is older than the Hindu-Arabic system. The system was vigesimal (base twenty), so it has twenty digits. The Mayas used a shell symbol to represent zero. Numerals were written vertically, with the ones place at the bottom. The Mayas had no equivalent of the modern decimal separator, so their system could not represent fractions.
The Thai numeral system is identical to the Hindu Arabic numeral system except for the symbols used to represent digits. The use of these digits is less common in Thailand than it once was, but they are still used alongside Hindu-Arabic numerals. The rod numerals, the written forms of counting rods once used by Chinese and Japanese mathematicians, are a decimal positional system able to represent not only zero but also negative numbers. Counting rods themselves predate Hindu-Arabic numeral system. The Suzhou numerals are variants of rod numerals

# Google searches on 10/4/2013 "The history of digital systems"

Digital Electronic Principles by Dr.Debashis De, Associate Professor at West Bengal University of Technology: - - "An introduction to the history of digital systems: The journey of digital electronics started in the year 1946 with the digital computer using vacuum tube technology. The term digit is derived from the counting operation of the computer. The twenty-first century is the digital world. Modern computers consist of digital components, starting from microprocessors to all other peripheral components. A binary digital circuit operates in two modes/states: ON state [1 (one)] and OFF state [0 (zero)]. These states are called binary states. These binary digits are called bits. In the binary digital world the logic lies between these two states. This makes the digital states discrete in nature, whereas the analog states are continuous". Digital Islands: - - "It is also important to understand the extent to which digital technology has evolved. The most significant advancement in the history of digital systems has been the proliferation of personal computers. There were many advancements that made this possible, but the introduction of the microprocessor in 1971 has revolutionized the way the world thinks about and uses computers. The applications in business and industry have evolved to the point that there are few areas that have not been impacted by digitalization. In addition, communications systems have made information much more accessible". TechExchange.com
"Integration in avionics hardware is traced from use of 16-transistor chips to emerging 100,000 gate chips, and attention is given to architectural considerations for future hardware". - TechExchange.com
Theodor Holm Nelson's talk about the future of digital marketing
The history of Torode's business, Digital Systems Inc.
"Indeed, the history of digital systems is one of rapid obsolescence and a lack of backward compatibility. The development of standards for document encoding, such as SGML and HTML, are at best partial solutions". - library.riphah.edu

# "Digital systems must":

- confront security issues
- include inputs and outputs
- plan on errors and resolve them
- have in band & on Channel (IBOC)
- be predefined to operate correctly
- be visualized
- account for signal skew
- be efficient & reliable

# "All digital systems include"

- some analog parts
- error detection's and corrections

# "The digital industry includes":

- offering a "freemium" or a 'get
- online data storage
- a claims processing and office management
- website production & user mgt
- software, -- computer games, -- videos
- websites & animation
- culture
- the internet, -- tv media
- senior figures from the worlds of art
- education & lifestyle
- creators, -- aggregate, -- advertisers
- intersectoral communication
- process improvement tools
- homecare technology

# Growth of Programmed Data Processors depicted by Digital Equipment Corporation from 1960 to 1980

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