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1 /9/ General dea More its and ytes inary umbers & uffman oding!!"#"$%&'()*+,-%$"+).'!/$/$")#'$/',//)/'+,' %/)/'+*'%'/)+-/)+)'%$'%'/"'&%/'%)6' $"-/.'%)6'! /)+-/)%.'&"#$9'-%#)/$"-9'%,#/9'-%9'+&+,9' :,,/)$9';'!!/$/$")#'6//)6'+)'/)+-/)+)'<':$'$/',/:&$' -:$'/'6",/$/.'"$'=%'6/$/$/6'+,')+$>'$/,/'"')+' +$"+)'*+,' +,$%'$/,/ ' // Larry Snyder, S What have we seen digital representations for?! olors W due in a week. Last W before midterm.! Letters! Logical alculations! umbers Positional otation!?")%,@'):-/,9'&"/'6/"-%&'):-/,9':/'!"#$%& '()#)*('' '' '!!"!#$#!%!"""#&#!%!""#&#"%!"##&#!%!# # ##$#!%!" ' ###&#!%!" ( ##&#"%!"! #&#!%!" "# '//$'$%$'$/'%/'"'')+$'D' #!!"!#$#!%)##&#!%*##&#"%(##&#!%!# # ##$#!%( ' #&#!%( ( #&#"%(! #&#!%( " # ase or radix inary umbers! Volunteers? need. in binary is in decimal Larry Snyder, S

2 /9/ More binary numbers lickers: Which one represents different numbers?. vs.. vs.. vs. D. vs. What about other bases for number systems?! index.htm What is binary addition? Let s clicker this logic out! What is the answer? + S... D..

3 /9/ Last week: First guest Lecture! Guest Lecture hursday: Lifelogging & Social Media! Prof. Whittaker's ome Page! esting on invited talks:! o homework on them but possible clicker questions or midterm questions that demonstrate! hat you were there! hat you were paying attention! hat you understood the presentation! ome prepared to ask questions! lickers. Prof. Whittaker Guest Lecture.! he main points of Professor Whittaker s guest lecture included that:. urrent capacity for digital storage make it possible to really do Lifelogging. Lifelogging is ethically and morally wrong and should be stopped. o make Lifelogs useful, all we have to do is just record everything D. ll of the above. one of the above!! lickers. hattyweb and Piccy Web Professor Whittaker s lecture included this graph. lickers What does the graph show?! his table from Prof. Whittaker s guest lecture shows:. est predictor of student s grade was GP coming into the class. ow much you used hatty & Piccy significantly improved your grade.. one of the above. D. ll of the above.. People often remember very little about an arbitrary day.. People who have been wearing a Senseam cannot remember everything.. n interface that combines the information from both the Senseam and GPS makes it possible to remember more about an arbitrary day D. Surprisingly, when we are talking about improving human memory, an interface showing where you went in your day works better than an interface with information from the Senseam.. ll of the above uffman oding: wiki/uffman_coding UF-: ll the alphabets in the world! F)"*+,-'G,%)*+,-%$"+)'+,-%$.''%' %,"%&/J="6$'/)+6")#'$%$'%)',/,//)$' //,@'%,%$/,'")'$/'F)"+6/'K%,%$/,' /$''!,,6 of them!!! '! $$.LL/)M=""/6"%M+,#L=""LFGJ''! FGJ'"'$/'6+-")%)$'%,%$/,'/)+6")#' *+,'$/'+,&6J"6/'/9'%+:)$")#'*+,' -+,/'$%)'%&*'+*'%&&'/'%#/M'! G/'()$/,)/$'P)#")//,")#'G%'+,/'Q(PG',/S:",/'%&&'()$/,)/$',+$++&'$+'"6/)$"*@' $/'/)+6")#':/6'*+,'%,%$/,'6%$%'! G/':+,$/6'%,%$/,'/)+6")#'-:$' ")&:6/'FGJM'

4 /9/ ow many bits for all of Unicode? here are,,6 different Unicode characters. f a fixed bit format (like ascii with its bits) where used, how many bits would you need for each character? (int: = )... D.. oding can be used to do ompression! What is DG?! he conversion of one representation into another! What is MPSS?! hange the representation (digitization) in order to reduce size of data (number of bits needed to represent data)! enefits! educe storage needed! onsider growth of digitized data.! educe transmission cost / latency / bandwidth! When you have a 6K dialup modem, every savings in S counts, SPD! lso consider telephone lines, texting What makes it possible to do ompression?! WDS: When is oding USFUL?! When there is edundancy! ecognize repeating patterns! xploit using! Dictionary! Variable length encoding! When uman perception is less sensitive to some information! an discard less important data ow easy is it to do it?! Depends on data! andom data! hard! xample:!?! rganized data! easy! xample:! "! W DS M?! here is universally best compression algorithm! t depends on how tuned the coding is to the data you have uffman ode: Lossless ompression! Use Variable Length codes based on frequency (like UF does)! pproach! xploit statistical frequency of symbols! What do M by that? W U!!!! LPS when the frequency for different symbols varies widely! Principle! Use fewer bits to represent frequent symbols! Use more bits to represent infrequent symbols uffman ode xample! dog cat cat bird bird bird bird fish Symbol Dog at ird Fish Frequency / / / / riginal ncoding bits bits bits bits uffman ncoding bits bits bit bits! xpected size! riginal! /" + /" + /" + /" = bits / symbol! uffman! /" + /" + /" + /" =. bits / symbol

5 /9/ uffman ode xample uffman ode lgorithm: Data Structures Symbol Dog at ird Fish Frequency / / / / riginal ncoding uffman ncoding bits bits bits bits bits bits bit bits ow many bits are saved using the above uffman coding for the sequence Dog at ird ird ird?... D..! inary (uffman) tree! epresents uffman code! dge! code ( or )! Leaf! symbol! Path to leaf! encoding! xample! =, =, =! Good when???!, less frequent than in messages! Want to efficiently build a binary tree uffman ode lgorithm verview! rder the symbols with least frequent first (will explain)! uild a tree piece by piece! ncoding! alculate frequency of symbols in the message, language! JUS U D DVD Y L UM F SYMLS! reate binary tree representing best encoding! Use binary tree to encode compressed file! For each symbol, output path from root to leaf! Size of encoding = length of path! Save binary tree uffman ode reating ree! lgorithm (ecipe)! Place each symbol in leaf! Weight of leaf = symbol frequency! Select two trees L and (initially leafs)! Such that L, have lowest frequencies in tree! Which L, have the lowest number of occurrences in the message?! reate new (internal) node! Left child! L! ight child!! ew frequency! frequency( L ) + frequency( )! epeat until all nodes merged into one tree uffman ree onstruction uffman ree Step : can first re-order by frequency

6 /9/ uffman ree onstruction uffman ree onstruction uffman ree onstruction uffman oding xample = = = = =! uffman code! nput!! utput! ()()() = = = = = = uffman ode lgorithm verview UP to here was a review of what we did last uesday! Decoding! ead compressed file & binary tree! Use binary tree to decode file! Follow path from root to leaf 6

7 /9/ uffman Decoding uffman Decoding uffman Decoding uffman Decoding uffman Decoding uffman Decoding 6

8 /9/ uffman Decoding uffman ode Properties! Prefix code! o code is a prefix of another code! xample! uffman( dog )!! uffman( cat )! // not legal prefix code! an stop as soon as complete code found! o need for end-of-code marker! ondeterministic! Multiple uffman coding possible for same input! f more than two trees with same minimal weight uffman ode Properties! Greedy algorithm! hooses best local solution at each step! ombines trees with lowest frequency! Still yields overall best solution! ptimal prefix code! ased on statistical frequency! etter compression possible (depends on data)! Using other approaches (e.g., pattern dictionary) uffman oding. nother example. uffman ree xample. Step uffman ree:!! =! =! =! =! =! =

9 /9/ licker: uffman ree: Which nodes can get combined next?. he brown node worth (, ) and the node worth. he node worth and the node worth. he brown node worth (,) and the node worth D. ll of the above uffman ree: uffman ree: Which nodes can get combined next?. he brown node worth (,, ) and the node worth. he brown node worth (,, ) and the node worth. he node worth and the node worth D. ll of the above uffman ree: uffman ree: Which nodes can get combined next?. he brown node worth (,, ) and the node worth. he brown node worth (,, ) and the node worth. he node worth and the node worth D. ll of the above 9

10 /9/ uffman ree: uffman ree: = = = = = = uffman ree: = = = = = =..... uffman ree: = = = = = =..... bits ow many bits would it take to store this message if every letter was represented with the same number of bits? You should first figure out how many bits it takes to represent 6 different values/ letters. = = = = = = uffman ode lgorithm verview! Decoding! ead compressed file & binary tree! Use binary tree to decode file! Follow path from root to leaf! FS XMPL D bits

11 /9/ uffman Decoding uffman Decoding uffman Decoding uffman Decoding uffman Decoding uffman Decoding 6

12 /9/ uffman Decoding DDG: nd example = = = = = = = uffman ode Properties! Prefix code! o code is a prefix of another code! xample! uffman( dog )!! uffman( cat )! // not legal prefix code! an stop as soon as complete code found! o need for end-of-code marker! ondeterministic! Multiple uffman coding possible for same input! f more than two trees with same minimal weight o code is prefix of another = = = = = = DDG: Your turn = = = = = = =? DDG: Your turn... D.. = = = = = = =?

13 /9/ uffman ode Properties! Greedy algorithm! hooses best local solution at each step! ombines trees with lowest frequency! Still yields overall best solution! ptimal prefix code! ased on statistical frequency! etter compression possible (depends on data)! ut needs look ahead, not prefix. omework : Data representations. Logic. inary umbers. S. uffman oding. S s S bits or bits? We use the bit table D'DD' D'D' DD'D' K' ' G' // Lawrence Snyder, S