| SECTION A |
- Boolean Algebra- Propositional logic, well formed formulae, truth values and interpretation of well formed formulae (wff), truth tables, satisfiable, unsatisfiable and valid formulae. Equivalence laws and their use in simplifying wffs, Binary valued quantities; basic postulates of Boolean algebra; operations AND, OR and NOT; truth tables, Basic theorems of Boolean algebra (e.g. duality, idempotence, commutativity, associativity, distributivity, operations with 0 and 1, complements, absorption, involution); De Morgan’s theorem and its applications; reducing Boolean expressions to sum of products and product of sums forms; Karnaugh maps (up to four variables).
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- Computer Hardware- Elementary logic gates (NOT, AND, OR, NAND, NOR, XOR, XNOR) and their use in circuits, Applications of Boolean algebra and logic gates to half adders, full adders, encoders, decoders, multiplexers, NAND, NOR as universal gates
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| SECTION B |
- Implementation of algorithms to solve problems- The students are required to do lab assignments in the computer lab concurrently with the lectures. Programming assignments should be done such that each major topic is covered in at least one assignment. Assignment problems should be designed so that they are sufficiently challenging. Students must do algorithm design, address correctness issues, implement and execute the algorithm in Java and debug where necessary
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- Programming in Java (Review of Class XI Sections B and C)- Note that items 4 to 13 should be introduced almost simultaneously along with classes and their definitions.
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- Objects- Objects as data (attributes) + behaviour (methods); object as an instance of a class, Constructors, Analysis of some real-world programming examples in terms of objects and classes, Basic input/output using Scanner and Printer classes from JDK; input/output exceptions, Tokens in an input stream, concept of whitespace, extracting tokens from an input stream (String Tokenizer class)
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- Primitive values, Wrapper classes, Types and casting: Primitive values and types: byte, int, short, long, float, double, boolean, char. Corresponding wrapper classes for each primitive type. Class as type of the object. Class as mechanism for user defined types. Changing types through user defined casting and automatic type coercion for some primitive types
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- Variables, Expressions: Variables as names for values; named constants (final), expressions (arithmetic and logical) and their evaluation (operators, associativity, precedence). Assignment operation; difference between left hand side and right hand side of assignment.
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- Statements, Scope: Statements; conditional (if, if else, if else if, switch case, ternary operator), looping (for, while, do while, continue, break); grouping statements in blocks, scope and visibility of variables
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- Methods: Methods (as abstractions for complex user defined operations on objects), formal arguments and actual arguments in methods; different behaviour of primitive and object arguments. Static method and variables. The this Operator. Examples of algorithmic problem solving using methods (number problems, finding roots of algebraic equations etc.).
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- Arrays, Strings: Structured data types – arrays (single and multidimensional), address calculations, strings. Example algorithms that use structured data types (e.g. searching, finding maximum/minimum, sorting techniques, solving systems of linear equations, substring, concatenation, length, access to char in string, etc.).
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- Recursion: Concept of recursion, simple recursive methods (e.g. factorial, GCD, binary search, conversion of representations of numbers between different bases)
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| SECTION C |
- Inheritance, Interface, Polymorphism, Data structures, Computational complexity: Inheritance; super and derived classes; member access in derived classes; redefinition of variables and methods in subclasses; abstract classes; class Object; protected visibility. Subclass polymorphism and dynamic binding, Interfaces in Java; implementing interfaces through a class; interfaces for user defined implementation of behaviour
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- Data structures: Basic data structures (stack, queue, circular queue, dequeue); implementation directly through classes; definition through an interface and multiple implementations by implementing the interface. Conversion of Infix to Prefix and Postfix notations, Single linked list (Algorithm and programming), binary trees, tree traversals (Conceptual).
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- Complexity and Big O notation: Concrete computational complexity; concept of input size; estimating complexity in terms of methods; importance of dominant term; constants, best, average and worst case.
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