This section covers Boolean logic (the mathematical basis of digital circuits) and database management — two fundamental areas of computer science that underpin hardware and data management respectively.
NOT: inverts input (1→0, 0→1). AND: output 1 only if both inputs are 1. OR: output 1 if at least one input is 1. NAND: NOT AND (output 0 only if both inputs 1). NOR: NOT OR (output 0 if any input 1). XOR: output 1 if inputs are different. Truth tables list all possible input combinations and their outputs. Logic circuits combine multiple gates. Trace through circuits by evaluating each gate from inputs to output.
Written using operators: AND (∧), OR (∨), NOT (¬ or overbar). Example: X = (A AND B) OR (NOT C). Simplify expressions using: De Morgan\'s laws, Boolean algebra rules. Build logic circuits from expressions: identify operators, connect gates. Build expressions from truth tables: find rows where output = 1, write expression for each row, combine with OR. Karnaugh maps (extended) can simplify complex expressions.
Database: organised collection of related data. Table: stores data about one entity. Record: one row (one instance). Field: one column (one attribute). Primary key: unique identifier for each record. Data types: TEXT, INTEGER, REAL, BOOLEAN, DATE. SQL queries: SELECT field1, field2 FROM TableName WHERE condition ORDER BY field ASC/DESC. Wildcards: LIKE \'A%\' (starts with A). Multiple conditions: AND, OR, NOT. Relational databases: multiple related tables linked by keys (foreign key references primary key of another table).
Logic gates are the fundamental building blocks of all digital circuits and processors. Every operation a computer performs — from adding numbers to running programs — is ultimately carried out by combinations of simple logic gates implemented as transistors on a chip. An ALU (Arithmetic Logic Unit) uses logic gates for addition, subtraction, and comparison. Memory (flip-flops) uses logic gates to store bits. The CPU\'s control unit uses logic gates to decode and execute instructions. Understanding logic gates helps you understand how hardware works at the most fundamental level. A modern CPU contains billions of transistors forming millions of logic gates.
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