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SYLLABUS CLASS XII

                                                COMPUTER SCIENCE (868)



                    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. Chain
                           rule, Modus ponens.

                       (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.
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