; Horner's Method Simulation ; written by Teresa Carrigan, 2004 globals [ start-x praise digits myDigits doneyet? number-of-digits base start-number] breeds [ digit arrow] digit-own [ digit-value] arrow-own [ largest ] patches-own [ name ] ; runs setup when program is first loaded to startup setup end ; makes the correct number of digits, and the red arrow ; initializes variables to setup locals [ here-x current n] ca set praise [ "You got it!" "Right!" "Correct" "Awesome!" "Perfect!" ] set digits [ "0" "1" "2" "3" "4" "5" "6" "7" "8" "9" "A" "B" "C" "D" "E" "F" ] set base 2 + random 15 set number-of-digits 4 + random 5 set myDigits [] set n 0 repeat base [ set myDigits lput (item n digits ) myDigits set n (n + 1) ] set start-x 7 set here-x 5 set n 0 set doneyet? false ; make a turtle for each digit set start-number "" repeat number-of-digits [ cct-digit 1 [ setxy here-x 0 set shape "circle" set color white set size 2 set label-color black set digit-value random base set label (word (item digit-value myDigits) " ") set start-number (word label start-number) ] set here-x (here-x - 1.5) ] ; start-number is a string equivalent to the digit pattern, with commas set start-number clean-input start-number set start-number add-commas start-number ; create red arrow cct-arrow 1 [ setxy here-x 0 set heading 90 set color red set shape "arrow" set largest int -1 ] ; create explanation bar at the bottom ask patches with [ pycor < -3 ] [ set pcolor blue ] ask patch-at 6 -4 [ set plabel "What is the smallest base in which" set plabel-color white set name 1 ] ask patch-at 6 -5 [ set plabel start-number + " would be a legal number?" set name 2 ] end ; step to the right, processing each digit that is found to one-step locals [ n ch answer] ask arrow [ ifelse ( xcor < 7) [ fd .5 if any? other-digit-here [ ask other-digit-here [ set n digit-value set ch label ] if n > largest [ ; found a larger digit than we had before set largest n ask patches with [ name = 1 ] [ ifelse n > 9 [set plabel "Largest digit found = " + ch + " = " + n ] [set plabel "Largest digit found = " + n ] ] ask patches with [ name = 2 ] [ set plabel "So base must be at least " + (n + 1) ] ] ] ] [ set doneyet? true ] ] if doneyet? [ ; all digits processed ask arrow [ set answer (largest + 1)] set answer add-commas (word "" answer) ask patches with [ name = 2 ] [ set plabel "Smallest legal base = " + answer ] ] end to show-again locals [ x] set doneyet? false ; determine where to put the arrow to start set x xcor-of min-one-of digit [ xcor ] set x x - 2 ; initialize arrow ask arrow [ setxy x 0 set heading 90 set largest int -1 ] end ; show all remaining steps to go locals [ answer ] ifelse not doneyet? [ one-step wait slow-motion ] [ ; display answer ask arrow [ set answer (largest + 1)] set answer add-commas (word "" answer) ask patches with [ name = 2 ] [ set plabel "Smallest legal base = " + answer ] stop ] end ; asks the user a quiz question to ask-other locals [ guess target question save-slow k ] set question start-number set guess user-input (word "What is the smallest base in which " question " would be a legal number?") set guess clean-input guess set guess read-from-string guess ; get target set save-slow slow-motion set slow-motion 0 while [ not doneyet?] [go] set slow-motion save-slow ask patches with [ name = 2 ] [ set k position "=" plabel set target substring plabel (k + 1) (length plabel) ] set target clean-input target set target read-from-string target ; is answer correct? ifelse guess = target [ user-message random-one-of praise ] [ user-message "I'm sorry, but the correct answer is " + target + "."] end ; removes blanks and commas, changes lower-case to upper-case to-report clean-input [guess] locals [ pos k upper lowerList] set guess remove " " guess set guess remove "," guess set lowerList ["a" "b" "c" "d" "e" "f"] foreach lowerList [ while [member? ? guess] [ set pos position ? guess set k position ? lowerList set upper (item (k + 10) digits) set upper word upper "" set guess replace-item pos guess upper ] ] report guess end ; add commas every three digits, so the user won't make copy errors to-report add-commas [ number ] locals [ save k ] set save "" set k 0 while [ (length number) > 0 ] [ set save (word last number save ) set number butlast number set k (k + 1) if (k = 3) and (length number > 0) [ set save (word "," save ) set k 0 ] ] set number save report number end ; ask a quiz question to quiz without-interruption [setup ] wait .5 ask-other end ; *** NetLogo Model Copyright Notice *** ; ; Copyright 2004 by Teresa W. Carrigan. All rights reserved. ; ; Permission to use, modify or redistribute this model is hereby granted, ; provided that both of the following requirements are followed: ; a) this copyright notice is included. ; b) this model will not be redistributed for profit without permission ; from Teresa W. Carrigan. ; Contact Teresa W. Carrigan for appropriate licenses for redistribution ; for profit. ; ; To refer to this model in academic publications, please use: ; Carrigan, T. (2004). Smallest Legal Base Simulation model. ; Blackburn College, Carlinville IL. ; ; In other publications, please use: ; Copyright 2004 by Teresa W. Carrigan. All rights reserved. ; ; *** End of NetLogo Model Copyright Notice *** @#$#@#$#@ GRAPHICS-WINDOW 3 10 388 316 7 5 25.0 1 18 1 1 1 CC-WINDOW 400 245 577 306 Command Center BUTTON 418 75 501 108 NIL setup NIL 1 T OBSERVER T SLIDER 418 141 591 174 slow-motion slow-motion 0 1 0.3 0.1 1 seconds BUTTON 503 108 591 141 quiz quiz NIL 1 T OBSERVER T BUTTON 502 75 591 108 go go T 1 T OBSERVER T BUTTON 418 108 502 141 NIL show-again NIL 1 T OBSERVER T @#$#@#$#@ WHAT IS IT? ----------- This model determines the smallest legal base for a random digit pattern. The quiz will test your understanding of this concept. HOW IT WORKS ------------ The arrow passes through the digits from one side to the other, remembering the largest digit it finds. The digit pattern will be legal in all bases that are larger than the largest digit found, so the smallest legal base is one more than that largest digit. HOW TO USE IT ------------- The setup button creates a random digit pattern. The slow-motion slider is an easy way to adjust the speed of the display. Set it to zero if you want to show the final result as quickly as possible. 0.3 is a good setting for most purposes. The go button does all remaining steps, at a speed determined by the slow-motion slider. This is useful when you do not need to take notes between each step, or do not wish to press the step button several times to get an answer. If you want to pause the demonstration, simply click the go button a second time and it will stop after it finishes the current step. You may then click go a third time to resume. The quiz button will generate a random digit pattern, and ask you to determine the smallest legal base. The show-again button starts the exact problem from the beginning. You may then click either the step button or the go button to see the same demonstration. THINGS TO NOTICE ---------------- The smallest legal base is always one more than the largest digit found in the digit pattern. If that digit is A, B, C, D, E or F, then the digit is converted to its decimal equivalent first. For example, if a digit pattern contains an F, then the smallest legal base would be 16, because F represents the decimal number 15. THINGS TO TRY ------------- Set slow-motion to 0.3, click setup, and then click go. Click setup, and then determine on paper what the answer would be. Click go to check your answer. EXTENDING THE MODEL ------------------- Modify the model to show fixed point representation; that is, specify a given number of digits to the right of the decimal place. Allow the user to input a starting digit pattern. NETLOGO FEATURES ---------------- Extensive use is made of "ask patches with". "other-digit-here" is used by the arrow to check the value of each digit. RELATED MODELS -------------- Horner's Method, Place Value Method, Counting in Other Number Bases CREDITS AND REFERENCES ---------------------- This model was written by Teresa W. Carrigan, 2004. Permission to use, modify or redistribute this model is hereby granted, provided that both of the following requirements are followed: a) this copyright notice is included. b) this model will not be redistributed for profit without permission from Teresa W. Carrigan. Contact Teresa W. Carrigan for appropriate licenses for redistribution for profit. To refer to this model in academic publications, please use: Carrigan, T. (2004). Smallest Legal Base Simulation model. Blackburn College, Carlinville, IL. In other publications, please use: Copyright 2004 by Teresa W. Carrigan. All rights reserved. FOR MORE INFORMATION -------------------- For more information, see one of the following textbooks: [1] Null, L. and Lobur, J. "Essentials of Computer Organization and Architecture", First Edition, Jones and Bartlett, page 38. [2] Dale, N. and Lewis, J. 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