This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: A C ourse O n C omputing F or C omputing S tudent L earning O bjective 1 1 A learning objective is something a student will understand and be able to continually use. William Shoaff January 5 , 2010 Text in blue jump to a section in the textbook where the topic is presented. Text in green jump to an external Web page, often Wikipedia . Name, Values, and Types: A name is a string over a finite alphabet . The name is used to write, pronounce, or call the value of some thing. Values can be organized into types where useful operations and functions can be computed. Alphabets: List several instances of an alphabet . B , D , H , E Strings: The set of all strings over an alphabet can be defined recursively: The empty string is a string; Each character c in the alphabet is a string; If s and t are strings then st is a string; Nothing else is a string. Types: A type is a set of values named by strings over a finite alphabet. Number Systems: A number system is a type for expressing numeric values and operations on them. Natural Numbers : The set N of discrete values { 0, 1, 2, . . . } with addition and multiplication. Integers : The set Z of discrete values { 0, 1, 2, . . . } with addition, subtraction, and multiplication. Rationals : The set Q of discrete values { a / b : a , b Z b 6 = } with addition, subtraction, multiplication, and division. Reals : The R is an uncountable set of continuous values that can defined using notions from mathematical analysis. Bases 2 , 10 and 16 : Common alphabets used for naming numeric values. Conversion Algorithms for Natural Numbers: Convert between names for the same value written in different languages Horners Rule : Use Horners rule to convert from binary or hexadecimal to decimal Remaindering : Use repeated remaindering to convert from decimal to binary or hexadecimal Integers Encodings: There are multiple methods to encode inte gers SignMagnitude Place an explicit plus + or minus symbol before the number + = 1 and = 0 in binary. Complement Notation represents positive and negative inte gers. Use complement and convert between it and decimal signedmagnitude notation a course on computing for computing student learning objective 2 Biased Notation Interpret the value of number written in bi ased notation . Floating Point Interpret the value of a number written in floating point notation . Data Structures A data structure organizes information for efficient processing. Sets A set is an unordered collection. Element Of Given a set X and an element x , compute the Boolean function ElementOf ( x , X ) If there is an algorithm for this function, the set X is decidable. Otherwise, x X is undecidable....
View Full
Document
 Fall '11
 Shoaff
 Math

Click to edit the document details