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A portion of the spring 2009 course materials for math 350: applied algebra, focusing on codes and ciphers. It covers topics such as decimal, binary, and hexadecimal number systems, conversion between them, and binary arithmetic. It also introduces morse code and ascii codes.
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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
n i n n i i
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 =
Hexadecimal Codes: Powers of 16: 160 =1, 16^1 = 16, 16^2 = 256, 16^3 = 4096, 16^4 = 65536, 16^5 = 1,048,576, 16^6 = 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 =
ASCII stands for American Standard Code for Information Interchange. Computers can only understand numbers, so an ASCII code is the numerical representation of a character such as 'a' or '@' or an action of some sort. ASCII was developed a long time ago and now the non-printing characters are rarely used for their original purpose. Below is the ASCII character table and this includes descriptions of the first 32 non-printing characters. ASCII was actually designed for use with teletypes and so the descriptions are somewhat obscure. If someone says they want your CV however in ASCII format, all this means is they want 'plain' text with no formatting such as tabs, bold or underscoring - the raw format that any computer can understand. This is usually so they can easily import the file into their own applications without issues. Notepad.exe creates ASCII text, or in MS Word you can save a file as 'text only' 22 4D 61 74 68 65 6D 61 74 69 63 73 20 69 73 20 74 68 65 20 71 75 65 65 6E 20 6F 66 20 74 68 65 20 73 63 69 65 6E 63 65 73 2E 22
Morse Code International Morse Code Braille
Homework #
Maple Explorations (Homework #1 cont.):
convert(101001, decimal, binary); convert(15, binary); convert(3985, hex); convert("E85", decimal, hex); Explain the Maple’s convert command. How do you use it to convert from decimal to binary or hex? From binary to decimal? From binary to hex? From hex to binary or decimal?
floor(12.674); floor(Pi); floor(-5.3); floor(exp(1)); floor(12); floor(-5); Explain Maple’s floor command.
ceil(12.674); ceil(Pi); ceil(-5.3); ceil(exp(1)); ceil(12); ceil(-5); Explain Maple’s ceil command.