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COMPUTER SCIENCE (868)
CLASS XII
There will be two papers in the subject:
Paper I: Theory……….. 3 hours….70 marks
Paper II: Practical…….. 3 hours….30 marks
PAPER I –THEORY – 70 MARKS SECTION A
1. Boolean Algebra
(a) 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. Propositional variables; the common logical
connectives (~ (not)(negation), ∧
(and)(conjunction), ∨ (or)(disjunction), ⇒
(implication), ⇔ (biconditional); definition
of a well-formed formula (wff); ` representation of simple word problems as wff (this can be used for motivation); the values true and false ; interpretation of a wff; truth tables; satisfiable, unsatisfiable and valid formulae.
Equivalence laws: commutativity of ∧ , ∨ ;
associativity of ∧ , ∨ ; distributivity; De
Morgan’s laws; law of implication (p ⇒ q ≡
~p ∨ q); law of biconditional ((p ⇔ q) ≡
(p ⇒ q) ∧ (q ⇒ p)); identity (p ≡ p); law of
negation (~ (~p) ≡ p); law of excluded
middle (p ∨ ~p ≡ true ); law of contradiction
(p ∧ ~p ≡ false ); tautology and contingency
simplification rules for ∧ , ∨. Converse,
inverse and contra positive.
(b) Binary valued quantities; basic postulates of Boolean algebra; operations AND, OR and NOT; truth tables.
(c) 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).
Verify the laws of Boolean algebra using truth tables. Inputs, outputs for circuits like half and full adders, majority circuit etc., SOP and POS representation; Maxterms & Minterms, Canonical and Cardinal representation, reduction using Karnaugh maps and Boolean algebra.
2. Computer Hardware
(a) Elementary logic gates (NOT, AND, OR, NAND, NOR, XOR, XNOR) and their use in circuits. (b) Applications of Boolean algebra and logic gates to half adders, full adders, encoders, decoders, multiplexers, NAND, NOR as universal gates. Show the correspondence between Boolean methods and the corresponding switching circuits or gates. Show that NAND and NOR gates are universal by converting some circuits to purely NAND or NOR gates.
SECTION B The programming element in the syllabus (Sections B and C) is aimed at algorithmic problem solving and not merely rote learning of Java syntax. The Java version used should be 5.0 or later. For programming, the students can use any text editor and the javac and java programs or any other development environment: for example, BlueJ, Eclipse, NetBeans etc. BlueJ is strongly recommended for its simplicity, ease of use and because it is very well suited for an ‘objects first’ approach.
3. 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. Self explanatory.
4. 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. While reviewing, ensure that new higher order problems are solved using these constructs. 5. Objects
(a) Objects as data (attributes) + behaviour (methods); object as an instance of a class. Constructors. (b) Analysis of some real-world programming examples in terms of objects and classes. (c) Basic input/output using Scanner from JDK; input/output exceptions. Tokens in an input stream, concept of whitespace.
6. 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. 7. 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.
8. 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.
9. Methods
Methods (as abstractions for complex user defined operations on objects), formal arguments and actual arguments in methods; Static method and variables. The this Operator. Examples of algorithmic problem solving using methods (number problems, finding roots of algebraic equations etc.).
10. Arrays, Strings Structured data types – arrays (single and multi- dimensional), 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.). Storing many data elements of the same type requires structured data types – like arrays. Access in arrays is constant time and does not depend on the number of elements. Address calculation (row major and column major), Sorting techniques (bubble, selection, insertion). Structured data types can be defined by classes – String. Introduce the Java library String class and the basic operations on strings (accessing individual characters, various substring operations, concatenation, replacement, index of operations). 11. Recursion Concept of recursion, simple recursive methods (e.g. factorial, GCD, binary search, conversion of representations of numbers between different bases). Many problems can be solved very elegantly by observing that the solution can be composed of solutions to ‘smaller’ versions of the same problem with the base version having a known simple solution. Recursion can be initially motivated by using recursive equations to define certain methods. These definitions are fairly obvious and are easy to understand. The definitions can be directly converted to a program. Emphasize that any recursion must have a base case. Otherwise, the computation can go into an infinite loop. The tower of Hanoi is a very good example of how recursion gives a very simple and elegant solution where as non-recursive solutions are quite complex.
SECTION C
Inheritance, Interface, Polymorphism, Data structures, Computational complexity
12. Inheritance, Interfaces and Polymorphism (a) Inheritance; super and derived classes; member access in derived classes; redefinition of variables and methods in
paper, correct output for unknown inputs available only to the examiner.
NOTE:
Algorithm should be expressed clearly using any standard scheme such as a pseudo code.
EQUIPMENT
There should be enough computers to provide for a teaching schedule where at least three-fourths of the time available is used for programming.
Schools should have equipment/platforms such that all the software required for practical work runs properly, i.e. it should run at acceptable speeds.
Since hardware and software evolve and change very rapidly, the schools may have to upgrade them as required.
Following are the recommended specifications as of now:
The Facilities:
- A lecture cum demonstration room with a MULTIMEDIA PROJECTOR/ an LCD and O.H.P. attached to the computer.
- A white board with white board markers should be available.
- A fully equipped Computer Laboratory that allows one computer per student.
- Internet connection for accessing the World Wide Web and email facility.
- The computers should have a minimum of 1 GB RAM and a P IV or higher processor. The basic requirement is that it should run the operating system and Java programming system (Java compiler, Java runtime environment, Java development environment) at acceptable speeds.
- Good Quality printers.
Software:
- Any suitable Operating System can be used.
- JDK 6 or later.
- Documentation for the JDK version being used.
- A suitable text editor. A development environment with a debugger is preferred (e.g. BlueJ, Eclipse, NetBeans). BlueJ is recommended for its ease of use and simplicity.
SAMPLE TABLE FOR PRACTICAL WORK
S. No.
Unique Identification Number (Unique ID) of the candidate
Assessment of Practical File
Assessment of the Practical Examination (To be evaluated by the Visiting Examiner only)
TOTAL MARKS
(Total Marks are to be added and entered by the Visiting Examiner)
30 Marks
Internal Evaluation 10 Marks
Visiting Examiner 5 Marks
Algorithm Java Program with internal Documentation
Hard Copy (printout)
Output
3 Marks 7 Marks 2 Marks 3 Marks
Name of the Visiting Examiner:_________________________________
Signature: _______________________________
Date:___________________________________
