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Octal

The octal numeral system, or oct for short, is the base-8 number system, uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping consecutive binary digits into groups of three. For example, the binary representation for decimal 74 is 1001010. Two zeroes can be added at the left: 1 001 010, corresponding the octal digits 1 1 2, yielding the octal representation 112. In the decimal system each decimal place is a power of ten. For example: 74 10 = 7 × 10 1 + 4 × 10 0 In the octal system each place is a power of eight. For example: 112 8 = 1 × 8 2 + 1 × 8 1 + 2 × 8 0 By performing the calculation above in the familiar decimal system we see why 112 in octal is equal to 64+8+2 = 74 in decimal; the Yuki language in California and the Pamean languages in Mexico have octal systems because the speakers count using the spaces between their fingers rather than the fingers themselves. It has been suggested that the reconstructed Proto-Indo-European word for "nine" might be related to the PIE word for "new".

Based on this, some have speculated that proto-Indo-Europeans used an octal number system, though the evidence supporting this is slim. In 1668 John Wilkins in An Essay towards a Real Character, a Philosophical Language proposed use of base 8 instead of 10 "because the way of Dichotomy or Bipartition being the most natural and easie kind of Division, that Number is capable of this down to an Unite". In 1716 King Charles XII of Sweden asked Emanuel Swedenborg to elaborate a number system based on 64 instead of 10. Swedenborg however argued that for people with less intelligence than the king such a big base would be too difficult and instead proposed 8 as the base. In 1718 Swedenborg wrote a manuscript: "En ny rekenkonst som om vexlas wid Thalet 8 i stelle wanliga wid Thalet 10"; the numbers 1-7 are there denoted by the consonants l, s, n, m, t, f, u and zero by the vowel o. Thus 8 = "lo", 16 = "so", 24 = "no", 64 = "loo", 512 = "looo" etc. Numbers with consecutive consonants are pronounced with vowel sounds between in accordance with a special rule.

Writing under the pseudonym "Hirossa Ap-Iccim" in The Gentleman's Magazine, July 1745, Hugh Jones proposed an octal system for British coins and measures. "Whereas reason and convenience indicate to us an uniform standard for all quantities. For tho' all nations count universally by tens yet 8 is a commodious number. In a treatise on Octave computation Jones concluded: "Arithmetic by Octaves seems most agreeable to the Nature of Things, therefore may be called Natural Arithmetic in Opposition to that now in Use, by Decades. In 1801, James Anderson criticized the French for basing the metric system on decimal arithmetic, he suggested base 8. His work was intended as recreational mathematics, but he suggested a purely octal system of weights and measures and observed that the existing system of English units was to a remarkable extent, an octal system. In the mid 19th century, Alfred B. Taylor concluded that "Our octonary radix is, beyond all comparison the "best possible one" for an arithmetical system."

The proposal included a graphical notation for the digits and new names for the numbers, suggesting that we should count "un, du, the, fo, pa, se, ki, unty-un, unty-du" and so on, with successive multiples of eight named "unty, thety, paty, sety and under." So, for example, the number 65 would be spoken in octonary as under-un. Taylor republished some of Swedenborg's work on octal as an appendix to the above-cited publications. Octal became used in computing when systems such as the UNIVAC 1050, PDP-8, ICL 1900 and IBM mainframes employed 6-bit, 12-bit, 24-bit or 36-bit words. Octal was an ideal abbreviation of binary for these machines because their word size is divisible by three. So two, eight or twelve digits could concisely display an entire machine word, it cut costs by allowing Nixie tubes, seven-segment displays, calculators to be used for the operator consoles, where binary displays were too complex to use, decimal displays needed complex hardware to convert radices, hexadecimal displays needed to display more numerals.

All modern computing platforms, use 16-, 32-, or 64-bit words, further divided into eight-bit bytes. On such systems three octal digits per byte would be required, with the most significant octal digit representing two binary digits. Octal representation of a 16-bit word requires 6 digits, but the most significant octal digit represents only one bit; this representatio

Lawrence Haward

Lawrence Warrington Haward was a noted art collector and writer, the second Curator of the Manchester City Art Gallery from 1914 to 1945. He was born in Westminster in London in 1878, the oldest son of Amy Cecilia née Nicholls and John Warrington Haward, a surgeon. In October 1897 he was admitted to King's College, taking his B. A. in 1900 and gaining his M. A. in 1904. He was the Librarian at the University of London, was on the musical staff of The Times. In 1914 Haward was appointed Curator of the Manchester Art Gallery having succeeded William Stanfield, the Gallery’s first Curator. Haward was to hold the post for over 30 years until his retirement in 1945. An "influential and astute collector", under Haward's direction the Gallery went through a period of great expansion which saw five new branch galleries opening across Manchester and the collection tripling in size. In addition, Haward was able to attract important gifts and bequests to the Gallery from noted collectors in the city or from others who had connections with Manchester.

These gifts included that of James Blair who in 1917 bequeathed a collection of paintings and watercolours, including an important collection of watercolours by Turner. In 1922 Mary Greg gave about 2,000 items to the Gallery including her collection of'Handicrafts of Bygone Times' as well as her collection of dolls and dolls’ houses. In 1923 Mary Greg further gifted to the Gallery her late husband Thomas Greg's collection of pottery from the Roman period to the early 19th-century, on loan to the Gallery since 1904. In 1920 Dr David Lloyd Roberts bequeathed his collection of paintings, prints and glass to the Gallery, while in 1934 John Yates bequeathed his extensive collection of jades, oriental ivories, enamels and Victorian paintings. In addition to these gifts, Haward bought contemporary art for the Gallery while in 1925 Charles Rutherston presented his modern art collection to the Gallery so that it could set up a loan service to local art colleges. In 1929 Haward was responsible for setting up the Industrial Art Collection, a collection of modern everyday objects designed to demonstrate the principles of good design.

Before his retirement in 1945 Haward obtained important art from both World Wars, thus creating one of the most important War Art collections outside London. Haward was a Trustee of the National Loan Collection Trust and was awarded the Honorary Degree of Master of Arts from the University of Manchester. In 1945 he launched a campaign to raise funds for the purchase of the extensive collection of husband and wife Cecil Willett Cunnington and Phillis Emily Cunnington. In 1947 their collection of costumes was acquired and the Gallery of Costume at Platt Hall was opened. Cecil Cunnington served as an Honorary Advisor to the collection. On his retirement Haward moved to Switzerland, he was cremated in that city. Haward, Lawrence.. Edward J. Dent: a bibliography. Cambridge University Press College. Haward, Lawrence.. Music in painting. New York: Pitman Pub. Corp. Haward, Lawrence.. Illustrated guide to the art collections in the Manchester corporation galleries. Manchester Art Galleries Committee, UK Haward, Lawrence..

The effect of war upon art and literature.

An Act to amend the Criminal Code (peremptory challenges)

An Act to amend the Criminal Code is an abbreviation of An Act to amend the Criminal Code, the Youth Criminal Justice Act and other Acts and to make consequential amendments to other Acts, passed in June 2019 by the Canadian Parliament at Ottawa. It was known as Bill C-75; some provisions of the Act came into force on 19 September 2019. It made the headlines when Justice Andrew Goodman of the Ontario Superior Court at trial ruled that the Act had infringed on an indigenous defendant's Charter Rights under Section 7; the first Trudeau administration had meant the Act to redress the power of defendants to dismiss potential jurors as part of their peremptory challenge rights granted as early as 1215 in the Magna Charta document. This was perceived by the Trudeau administration as needless discrimination and thus, in the 21st-century scramble to equalize society, needed to be stricken from collective memory; the need to rectify the law had become apparent to Liberal watchers of the death of Colten Boushie as a result of his 9 August 2016 trespass on the farm of Gerald Stanley, when they perceived racism to be evident in Stanley's 9 February 2018 acquittal.

The OSC case is known as R v Dale King. A learned commentator wrote, before the 19 September implementation, that the elimination of peremptory challenges "defeats the intended purpose"