EX OR gate

Duration: 11 min

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Module outline

  1. General Intelligence & Reasoning: Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Logical Sequence Of Words, Syllogisms, Venn Diagram, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Data Sufficiency, Puzzle Solving (Puzzles), Data Arrangement, Cubes & Dices, Calendar, Clock, Arithmetic, Number System, HCF LCM, Verbal Analogy (Word Based Analogy), Visual Recognition and Figure Completion, Paper Folding and Cutting, Transformation of Shapes, Clocks and Calendars, Direction Sense, Cubes and Dice, Patterns in Two-Dimensional Figures, Seating Arrangements, Analogy and Classification, Logical Deduction and Induction, Alphabet and Word Tests, Mathematical Operations, Series Completion, Simplification and Approximation, Coding and Decoding, Numerical Reasoning, Assembling and Grouping of Shapes, Three-Dimensional Patterns and Visualization, Vocabulary, Number System, Averages, Mixtures and Alligation, Simple and Compound Interest, Percentages, Algebra, Speed, Time and Distance, Seating and Arrangement Puzzles, Traverse Surveying, Order, Ranking and Sequence, Constraint Puzzles, Syllogisms and Venn Diagrams, Reading Comprehension, Critical Reasoning, Permutations and Combinations, Narrative Sequencing, Project Monitoring, Resources and Safety, Profit, Loss and Discount, Ratio and Proportion, Time and Work, Mensuration, Data Interpretation, Powers, Surds and Logarithms, Sequences and Series, Articles and Determiners, Sentence Completion, Data Sufficiency, Blood Relations, Simple Interest and Compound Interest, Mixture and Alligation, Sequence and Series (Series), Speed Time and Distance, Algebra, Profit and Loss, Powers and Exponents (Surds and Indices), Permutation and Combination
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  3. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus, Probability, Statistics, Signal Space and Optimum Detection, Probability, Statistics
  4. Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep, Number Systems and Codes, Registers and Counters, Boolean Algebra and Logic Gates, Microprocessors and Microcontrollers, Logic Families and CMOS Logic, Microprocessors, Logic Gates and Boolean Algebra, Minimization of Boolean Functions, Timing, Hazards and Testing, Logic Families, Combinational Logic Design, Arithmetic Circuits, Waveform Generators and Timer Circuits, Semiconductor Memories and Programmable Logic Devices, Combinational Logic Circuits, Latches and Flip-Flops, Finite State Machines, Sequential Circuits and State Machines, Minimization of Boolean Functions, Arithmetic Circuits, Latches and Flip-Flops, Number Systems and Codes, Registers and Counters
  5. Computer Organisation & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer, Register Transfer and Microoperations, Semiconductor Memories and Programmable Logic, Processor Organization and Instructions, Memory Hierarchy and Input/Output, Registers and Counters
  6. Programming & Data Structures: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, HTML Basics, OOPS with C++, Java, Object Oriented Technology
  7. Databases: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization
  8. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  9. Theory of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory
  10. Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
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  13. Full Length Mock Tests:
  14. Sectional Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video delivers a detailed lecture on the Exclusive-OR (EX-OR) logic gate, covering its definition, truth tables, and fundamental Boolean properties. It begins by defining the 2-input EX-OR gate, where the output is high only if inputs differ, and presents the corresponding algebraic expression and truth table. The lesson then expands to a 3-input configuration, establishing the rule that the output is high when the count of high inputs is odd. Subsequently, the instructor derives four key properties involving constants and variables, such as the identity and complement laws. The session concludes with a rigorous algebraic demonstration of the commutative and associative laws for the EX-OR operation.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the EX-OR gate with the on-screen text stating, 'For two inputs, output will be high if and only if both the input values are different.' He displays the algebraic formula $a \oplus b = a'.b + a.b'$ and a truth table with columns for Input A, Input B, and Output Y. He systematically fills the table, showing that inputs (0,0) and (1,1) yield 0, while (0,1) and (1,0) yield 1. To visualize this, he draws a Venn diagram with two overlapping circles, shading the non-overlapping regions to represent the symmetric difference. He also sketches the standard logic symbol for the EX-OR gate, noting the curved input side. The instructor points to the formula $a \oplus b = a'.b + a.b'$ to reinforce the algebraic representation.

  2. 2:00 – 5:00 02:00-05:00

    The lecture transitions to a 3-input EX-OR gate, with the slide text explaining, 'The XOR gate is a digital logic gate that gives High as output when the number of inputs High are odd.' A truth table for inputs A, B, and C is presented. The instructor fills the output column based on the odd-parity rule: for inputs (0,0,0) the output is 0; for (0,0,1) it is 1; for (0,1,0) it is 1; for (0,1,1) it is 0; for (1,0,0) it is 1; for (1,0,1) it is 0; for (1,1,0) it is 0; and for (1,1,1) it is 1. He writes the resulting sequence of outputs as 0, 1, 1, 0, 1, 0, 0, 1, emphasizing the pattern of odd numbers of 1s. He uses a pen to mark the 1s in the input columns to count them.

  3. 5:00 – 10:00 05:00-10:00

    The instructor details four specific properties of the EX-OR gate using a slide with numbered points. First, 'EX-OR with ZERO give same,' deriving $(a \oplus 0) = a'.0 + a.0' = 0 + a = a$. Second, 'EX-OR with ONE give comp,' deriving $(a \oplus 1) = a'.1 + a.1' = a' + 0 = a'$. Third, 'EX-OR with SAME give zero,' deriving $(a \oplus a) = a'.a + a.a' = 0 + 0 = 0$. Fourth, 'EX-OR with COMPLEMENT give one,' deriving $(a \oplus a') = a'.a' + a.a = a' + a = 1$. He also notes that the idempotent law does not apply, writing $(a \oplus a) eq a$. He begins proving the commutative law by writing $a \oplus b = a'b + ab'$ and showing it equals $b \oplus a$. The slide lists these properties as numbered points 1 through 4, with corresponding logic gate diagrams next to each equation.

  4. 10:00 – 11:27 10:00-11:27

    The final segment focuses on proving the associative law for EX-OR gates. The instructor writes the equation $((a \oplus b) \oplus c) = (a \oplus (b \oplus c))$ on the board. He proceeds to expand the left-hand side algebraically, substituting the definition of EX-OR into the expression. He writes out the full Boolean expansion, showing terms like $a'b'c + a'bc' + ab'c' + abc$. He performs similar expansion for the right-hand side to demonstrate that both sides result in the same set of minterms, thereby proving the associative property holds true for the EX-OR operation. The board becomes filled with red and black ink as he works through the complex algebraic steps.

The video provides a structured progression from basic definitions to complex algebraic proofs. It starts with the fundamental behavior of the 2-input gate, moves to the generalized 3-input parity check, and then solidifies understanding through specific properties involving constants and variables. The lesson culminates in formal proofs of commutativity and associativity, ensuring students understand not just how the gate works, but why it behaves according to Boolean algebra rules.

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