Download Math 350: Applied Algebra - Codes & Ciphers Spring 2009 - Prof. Julie M. Clark and more Assignments Mathematics in PDF only on Docsity! Math 350: Applied Algebra Codes & Ciphers Spring 2009 Codes – Class 1 Decimal Binary Hexadecimal Decimal Binary Hexadecimal 0 8 1 9 2 10 3 11 4 12 5 13 6 14 7 15 Binary ‘Words’ 1 2 1 0 2 0 ( ) 2 n i n n i i b b b b b b Converting from binary to decimal: (1101)2 = (10101)2 = (111)2 = (1110)2 = (111111)2 = How can you tell a binary number is odd? Even? Converting from decimal to binary: 12310 = 5410 = Binary arithmetic: Addition: (10110)2 + (1111)2 = Multiplication: (1011)2 * (101)2 = Long division: 2 2(101101) (1101) = Page 1 Math 350: Applied Algebra Codes & Ciphers Spring 2009 Hexadecimal Codes: Powers of 16: 160 =1, 161 = 16, 162 = 256, 163 = 4096, 164 = 65536, 165 = 1,048,576, 166 = 1,6777,216, 167 = 268,435,456, … Converting binary to hex: (1011001011101000101101111)2 = (1011000111000101)2 = Converting hex to binary: (5F90A)16 = (3D7)16 = Converting hex to binary: (5F90A)16 = (3D7)16 = Converting decimal to hex & vice versa: A79B)16 = 5000 = Page 2 Math 350: Applied Algebra Codes & Ciphers Spring 2009 Morse Code International Morse Code Braille Page 5 Math 350: Applied Algebra Codes & Ciphers Spring 2009 References: Applied Algebra: Codes, Ciphers, and Discrete Algorithms. Darel W. Hardy and Carol L. Walker. Prentice Hall, NJ, 2003. Web sites: http://morsecode.scphillips.com//index.html http://www.omnicron.com/~ford/java/NMorse.html http://freenet.msp.mn.us/people/calguire/morse.html http://www.omniglot.com/writing/braille.htm\ http://www.cnib.ca/eng/braille_information/louis_braille.htm http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Hollerith.html http://homepages.cwi.nl/~dik/english/codes/80col.html Page 6 Math 350: Applied Algebra Codes & Ciphers Spring 2009 Homework #1 1. a) Convert 45 to binary. b) Convert 122 to binary. c) Convert (10101011100001110101001101010100)2 to hexadecimal. d) Convert (5AB92)16 to binary. e) Convert (43BD)16 to decimal. f) Convert 50927341 to hexadecimal. g) Compute (2B)16 * (C1F)16 and express the result in hexadecimal notation. h) Compute (1011011)2 * (10111)2. i) Compute 2 2(1110001) (1011) using binary long division. 2. Convert the following sequence of (decimal) ASCII codes into an English sentence. 34 66 108 97 99 107 32 104 111 108 101 115 32 97 114 101 32 119 104 101 114 101 32 71 111 100 32 100 105 118 105 100 101 100 32 98 121 32 122 101 114 111 46 34 45 83 116 101 112 104 101 110 32 87 114 105 103 104 116 3. Use the web site: http://www.omnicron.com/~ford/java/NMorse.html to interpret the following message: ▪ ▬ ▬ ▬ ▪ ▬ ▬ ▪ ▬ ▪ ▬ ▪ ▪ ▪ ▬ ▪ ▬ ▪ ▬ ▬ ▬ ▪ ▬ ▪ ▪ ▪ ▬ ▪ ▪ ▪ ▬ ▬ ▪ ▪ ▬ ▬ ▬ ▬ ▬ ▪ ▬ ▪ ▪ ▪ ▪ ▪ ▬ ▪ ▪ ▪ ▪ ▬ ▪ ▪ ▪ ▪ ▬ ▬ ▪ ▪ ▪ ▪ ▪ ▬ ▪ ▬ ▪ ▪ ▪ ▪ ▬ ▪ ▪ ▬ ▬ ▪ ▪ ▬ ▪ ▪ ▬ ▪ ▬ ▪ ▪ ▬ ▪ ▬ ▬ ▪ ▬ ▬ ▪ ▪ ▬ ▪ ▪ ▪ ▪ ▬ ▬ ▪▪ ▬ ▪ ▬ ▪ ▪ ▪ ▬ ▬ ▪ ▬ ▬ ▬ ▪ ▬ ▪ ▬ ▪ ▬ ▪ ▪ ▬ ▪ ▪ ▬ ▪ ▪ ▪ (You can type Morse code into the Input box using "." for a dot and "-" or "_" for a dash. Letters are separated by spaces and words by "/" or "|".) 4. Translate the following phrase adapted from the novel The Little Prince by Antoine de Saint-Exupéry. Page 7
