By David Salomon

In 1829, Louis Braille, a tender organist in a Paris church, blind because age three, invented the well known code for the blind, nonetheless in universal use this day around the globe and named after him. Braille himself converted his code in 1834, and there were a number of ameliorations given that. besides the fact that, the fundamental layout of this code, the place each one personality is represented by means of a bunch of three x 2 dots, has remained intact. The dots are embossed on thick paper and every could be raised or flat (i. e. , current or absent). each one dot is as a result resembling one little bit of details. accordingly, the Braille code (Figure 1) is a 6-bit code and will as a result signify sixty four symbols (the code of six flat dots exhibits a clean space). Braille's fans prolonged the services of his code in numerous methods. One im­ portant extension is contractions. those are letters that, after they stand by myself, suggest phrases. for instance, the letter "b" status by myself (or with punctuation) ability the note "but," the letter "e" status on my own ability "every," and "p" potential "people. " one other extension is short-form phrases. those are combos of 2 or extra codes that suggest a whole observe (short-form phrases may possibly comprise contractions). for instance, "ab" capacity "about," "rcv" capacity "receive," and "(the)mvs" capability "themselves. " (The "the" in parentheses is a contraction, dots 2-3-4-6. ) determine 2 exhibits a few examples of those exact codes.

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6. 1356 ---+ o. Symbol "u" selected. Low = 7500+(9999-7500+1)xO/lO = 7500. High = 7500+(9999-7500+1)x1/lO-1 7749. After the 7 is shifted out, we have Low=5000, High=7499, and Code=5337. 49 is x is = 7. 3516 ---+ 1. Symbol "M" is selected. Low = 5000+(7499-5000+1)x1/10 = 5250. High = 5000+(7499-5000+1)x2/10-1 = 5499. After the 5 is shifted out, we have Low=2500, High=4999, and Code=3375. 8. 5036 ---+ 3. Symbol "I" is selected. Low = 2500+(4999-2500+1) x2/lO = 3000. High = 2500+(4999-2500+1) x4/lO-1 = 3499.

This is done to remove any ambiguity when the line is decoded on the receiving end. After reading the EOL for the previous line, the receiver assumes that the new line starts with a run of white pels, and it ignores the first of them. Examples: 1. The 14-pelline 1-1-1-1 I 1_1_1 I I I I I I Iis coded as the run lengths lw 3b 2w 2b 7w EOL, which become 00011111010111111111111000000000001. The decoder ignores the single white pel at the start. 2. The line I I 1-1-1-1-1-1 I I I I 1-1-1 is coded as the run lengths 3w 5b 5w 2b EOL, which becomes the binary string 100010011111001111000000000001.

The property illustrated here exists for any tree where a node contains the sum of its children. Statistics are no substitute for judgment. 5 Adaptive Huffman Coding The Huffman method assumes that the frequencies of occurrence of all the symbob of the alphabet are known to the compressor. In practice, the frequencies are seldom, if ever, known in advance. One solution is for the compressor to read the original data twice. The first time it just calculates the frequencies. The second time it compresses the data.

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