6.4 Introduction to digital electronics and logic gates

Digital electronics revolutionized technology, replacing analog systems with discrete signals. Logic gates, the building blocks of digital circuits, process binary data using simple operations like AND, OR, and NOT.

Combinational logic design uses Boolean algebra to create complex circuits from basic gates. Universal gates like NAND and NOR can implement any logic function, simplifying circuit design and manufacturing processes.

Analog vs Digital Signals

Continuous vs Discrete Signals

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• Analog signals take on continuous values within a range while digital signals have discrete, finite set of possible values
• Analog signals represent data as continuous waveforms whereas digital signals use series of binary digits (0s and 1s)
• Human voice and natural sounds exemplify analog signals while computer data and digital audio files demonstrate digital signals
• Analog-to-digital converters (ADCs) transform analog to digital signals
• Digital-to-analog converters (DACs) perform the reverse process, converting digital to analog

Advantages of Digital Signals

• Digital signals prove less susceptible to noise and interference compared to analog counterparts
• Enhanced reliability for long-distance transmission and storage characterizes digital signals
• Digital signals facilitate easier signal processing, data compression, and error correction
• Improved signal quality over long distances distinguishes digital from analog transmission (telephone lines)
• Digital signals allow for perfect copies to be made without degradation (CDs vs cassette tapes)

Logic Gates and Their Functions

Basic Logic Gates

• AND gate outputs logical 1 only when all inputs are 1, otherwise outputs 0
• OR gate outputs logical 1 if at least one input is 1, outputs 0 only when all inputs are 0
• NOT gate (inverter) produces output opposite of single input
• NAND gate outputs logical 0 only when all inputs are 1, inverse of AND gate
• NOR gate outputs logical 1 only when all inputs are 0, inverse of OR gate
• XOR (Exclusive OR) gate outputs logical 1 when number of 1s at inputs is odd, otherwise outputs 0

Truth Tables and Gate Symbols

• Truth tables represent input-output relationships of logic gates
• Tables show all possible combinations of inputs and corresponding outputs
• Standard symbols used to represent logic gates in circuit diagrams (AND symbol resembles D shape)
• Input lines typically drawn on left side of gate symbol, output on right
• Multiple input gates often represented with additional input lines (3-input AND gate)

Combinational Logic Circuit Design

Boolean Algebra Fundamentals

• Boolean algebra analyzes and designs digital circuits based on George Boole's principles
• Basic Boolean operations include AND (·), OR (+), and NOT ('), corresponding to logic gates
• Boolean expressions simplify using laws and theorems (commutative, associative, distributive)
• De Morgan's theorems prove essential for simplifying expressions and converting between gate types
• Boolean algebra applies to switching circuits and computer logic (computer memory circuits)

Design Techniques and Tools

• Karnaugh maps (K-maps) graphically simplify Boolean expressions
• K-maps minimize number of logic gates required in circuit design
• Combinational logic circuits designed by deriving Boolean expressions from truth tables or problem statements
• Don't-care conditions used to further simplify expressions and reduce circuit complexity
• Computer-aided design (CAD) tools assist in complex circuit design and optimization (Quartus Prime)

Logic Function Implementation with Universal Gates

NAND and NOR as Universal Gates

• NAND and NOR gates considered universal due to ability to implement any Boolean function
• Process involves expressing functions as AND, OR, and NOT operations
• Convert operations to equivalent NAND or NOR gate configurations
• NAND gates create NOT, AND, and OR gates as building blocks for complex functions
• NOR gates similarly produce NOT, AND, and OR gates for alternative implementation
• Universal gates lead to standardized circuit designs (integrated circuit manufacturing)

Implementation Techniques

• Bubble pushing technique simplifies logic circuits by manipulating inverter (NOT gate) placement
• Particularly useful when working with universal gates to optimize designs
• Choice between NAND and NOR implementation depends on available technology, power consumption, and propagation delay
• NAND gates often preferred in CMOS technology due to simpler structure (fewer transistors)
• NOR gates sometimes favored in certain applications for speed or compatibility reasons (memory cells in SRAM)