Coding-Decoding Trick: Memorize the forward and backward positional values of the English alphabet. (Forward: A=1...Z=26, Backward: A=26...Z=1). Use the EJOTY rule (E=5, J=10, O=15, T=20, Y=25).

Direction Sense: Always draw a small crosshair (N up, S down, W left, E right). Remember Pythagoras theorem H2 = P2 + B2 for shortest distance problems.

Time & Work: Use the LCM (Least Common Multiple) method instead of fractions. If A does a job in 10 days, B in 15 days. LCM(10,15) = 30 total units of work. A's efficiency = 3 units/day, B's = 2 units/day. Together = 5 units/day. Time = 30/5 = 6 days.

Profit & Loss: Always assume Cost Price (CP) = 100% unless specified. Selling Price (SP) = CP ± Profit/Loss%.
Discount is always calculated on Marked Price (MP).

Mirror Images: Left becomes Right, Right becomes Left. Top and Bottom remain the same.

Water Images: Top becomes Bottom, Bottom becomes Top. Left and Right remain the same.

Dice Rules: If two dice positions share one common face, rotate clockwise from the common face to find opposite pairs. If they share two common faces, the remaining unmatched faces are opposite to each other.

Von Neumann vs Harvard: Von Neumann uses a single memory space and bus for both data and instructions (causes Von Neumann bottleneck). Harvard uses separate memory and buses for data and instructions, allowing simultaneous fetching.

RISC vs CISC:
- RISC (Reduced Instruction Set Computer): Simple, highly optimized instructions, mostly single cycle. Uses hardwired control unit. Load/Store architecture (only specific instructions access memory). Many registers.
- CISC (Complex Instruction Set Computer): Complex instructions, multi-cycle execution. Uses microprogrammed control unit. Fewer registers.

8086 Architecture: A 16-bit microprocessor. Internally divided into two independent functional units:

• Bus Interface Unit (BIU): Handles all data and addresses on the buses for the EU. Contains a 6-byte instruction queue, Segment Registers (CS, DS, SS, ES), and Instruction Pointer (IP). Generates 20-bit physical address: Physical Address = (Segment * 10H) + Offset.
• Execution Unit (EU): Decodes and executes instructions. Contains the ALU, General Purpose Registers (AX, BX, CX, DX), Pointers (SP, BP), and Index Registers (SI, DI).

Memory Mapped I/O vs I/O Mapped I/O: In Memory Mapped, I/O devices share the same address space as memory; standard memory instructions manipulate I/O. In I/O mapped, separate IN/OUT instructions are used.

DMA (Direct Memory Access): Allows hardware subsystems to access main system memory independently of the CPU. The CPU grants the bus to the DMA controller, significantly speeding up bulk data transfers (like disk to memory).

Combinational Logic: Output depends solely on the current input. Examples: Adders (Half, Full), Multiplexers (Data Selectors), Decoders, Encoders.

Sequential Logic: Output depends on current input AND past state (requires memory/clock). Built using Latches and Flip-Flops.

• SR Flip-Flop: Set/Reset. S=1, R=1 is an invalid state.
• JK Flip-Flop: Solves SR invalid state. J=1, K=1 causes the output to toggle.
• D Flip-Flop: Data/Delay. Output follows input at the clock edge. Used in registers.
• T Flip-Flop: Toggle. Used in counters.

Semiconductors: N-type (doped with pentavalent impurities, majority carriers: electrons). P-type (doped with trivalent impurities, majority carriers: holes). PN Junction forms a diode (allows current in one direction).

BJT (Bipolar Junction Transistor): Current controlled device. Modes of operation: Active (amplifier), Saturation (closed switch), Cut-off (open switch).

Modulation: Superimposing a low-frequency message signal onto a high-frequency carrier wave.

• AM (Amplitude Modulation): Carrier amplitude varies. Prone to noise. Bandwidth = 2 * Message Frequency.
• FM (Frequency Modulation): Carrier frequency varies. Highly resistant to amplitude noise.

• Waterfall: Sequential, strictly phased. Good for small projects with clearly defined, unchanging requirements. Rigid and poor for dynamic projects.
• Prototyping: Building a simplified version of the system to understand requirements before actual coding.
• Spiral (Risk-Driven): Combines prototyping and waterfall. Emphasizes risk analysis at each iteration loop.
• Agile: Iterative, incremental. Highly adaptable to changing requirements. Scrums and Sprints are common implementations.

Coupling and Cohesion: The golden rule of software design is to aim for High Cohesion (modules perform a single, well-defined task) and Low Coupling (minimal dependencies between different modules).

Cost Estimation (COCOMO): Constructive Cost Model by Barry Boehm. Uses Lines of Code (LOC) to estimate Effort (Person-Months) and Development Time.

Testing Methodologies:

• Unit Testing: Testing individual components (usually by developers). White-box.
• Integration Testing: Testing combined components to find interface defects (Top-down or Bottom-up).
• System/Acceptance Testing: Testing the entire system against requirements (Alpha/Beta testing). Black-box.
• Regression Testing: Re-testing after fixes or updates to ensure no new bugs were introduced.

Keys: Primary Key (Unique, Not Null), Foreign Key (Maintains referential integrity), Candidate Key (Minimal set of attributes to uniquely identify a row).

SQL Joins: INNER JOIN (matches in both), LEFT JOIN (all from left, matched from right), RIGHT JOIN (all from right, matched from left), FULL OUTER JOIN (all records from both).

The process of organizing data to minimize redundancy and dependency anomalies (Insert, Update, Delete anomalies).

• 1NF: All attributes must be atomic (no multi-valued attributes or repeating groups).
• 2NF: Must be in 1NF AND no partial dependency (no non-prime attribute should depend on part of a composite primary key).
• 3NF: Must be in 2NF AND no transitive dependency (non-prime attributes must depend ONLY on the primary key).
• BCNF (Boyce-Codd NF): A stricter 3NF where for every functional dependency X → Y, X must be a superkey.

ACID Properties:

• Atomicity: "All or nothing." A transaction completes entirely or not at all.
• Consistency: The database must transition from one valid state to another.
• Isolation: Concurrent transactions do not interfere with each other.
• Durability: Once committed, changes are permanent, even after a system crash.

Concurrency Control: Techniques like Two-Phase Locking (2PL) and Timestamp ordering prevent issues like the Lost Update problem, Dirty Reads, and Unrepeatable Reads.

Chomsky Hierarchy: Classifies formal languages.

• Type 3 (Regular Languages): Recognized by Finite Automata (DFA/NFA). Generated by Regular Grammars. Used in Lexical analysis.
• Type 2 (Context-Free Languages): Recognized by Pushdown Automata (PDA). Generated by Context-Free Grammars (CFG). Used in Syntax analysis/Parsing.
• Type 1 (Context-Sensitive Languages): Recognized by Linear Bounded Automata (LBA).
• Type 0 (Recursively Enumerable): Recognized by Turing Machines. Unrestricted grammars.

Pumping Lemma: A mathematical proof technique used exclusively to prove that a specific language is NOT regular (or not context-free).

Complexity: P problems are solvable in polynomial time. NP problems have solutions verifiable in polynomial time. NP-Complete are the hardest problems in NP.

1. Lexical Analysis (Scanner): Reads source code character by character, groups them into meaningful sequences called Tokens. Removes whitespace and comments. Uses Regular Expressions and DFAs. (Tool: Lex)
2. Syntax Analysis (Parser): Takes tokens and builds a Parse Tree based on a Context-Free Grammar. Checks for syntax errors. (Tool: Yacc/Bison)
3. Semantic Analysis: Checks for semantic errors like type mismatches, undeclared variables. Gathers type info into the Symbol Table.
4. Intermediate Code Generation (IR): Creates machine-independent code (e.g., Three-Address Code).
5. Code Optimization: Improves IR to make it faster/smaller (e.g., dead code elimination, loop unrolling).
6. Target Code Generation: Converts optimized IR into machine code or assembly for a specific architecture, assigning registers.

Transformations: Handled using homogeneous coordinates (matrix multiplication). Translation (shifting), Scaling (resizing), Rotation (spinning around origin), Shearing, and Reflection.

Projections: Mapping 3D objects onto a 2D screen.

• Parallel Projection: Projection lines are parallel. Preserves relative dimensions. Used in engineering drawing (Orthographic).
• Perspective Projection: Projection lines converge at a center of projection. Objects farther away appear smaller. Highly realistic.

Cryptography: Symmetric key (same key for encrypt/decrypt, e.g., AES, DES) vs Asymmetric key (public key encrypts, private key decrypts, e.g., RSA). Used for network security, confidentiality, and non-repudiation.

Distributed Computing & Clusters: Multiple independent computers appearing as a single coherent system to the user. High availability and fault tolerance. Remote Procedure Call (RPC) allows execution of code on a remote server as if it were local.