Concept Taxonomy

This document defines the categorical taxonomy for organizing the 410 concepts in the Digital System Design learning graph.

Taxonomy Categories

Category Name	TaxonomyID	Description
Foundation Concepts	FOUND	Core foundational concepts that introduce digital systems and basic terminology
Number Systems	NUMSYS	Concepts related to different number bases, positional notation, and representations
Number Conversions	CONV	Techniques and methods for converting between different number systems
Binary Arithmetic	ARITH	Binary addition, subtraction, multiplication, division, and signed operations
Boolean Fundamentals	BOOLF	Basic Boolean algebra concepts, variables, constants, and operations
Logic Gates	GATES	Physical implementations of Boolean operations as logic gates
Boolean Theorems	THEOR	Boolean algebra laws, theorems, and simplification techniques
Boolean Forms	FORMS	Sum of products, product of sums, literals, and expression forms
Combinational Circuits	COMB	Combinational logic design, analysis, and synthesis
Arithmetic Circuits	ACIR	Adders, subtractors, comparators, and arithmetic circuit implementations
Canonical Forms	CANON	Minterms, maxterms, canonical SOP/POS, and standard forms
Karnaugh Maps	KMAP	K-map structure, simplification techniques, and optimization methods
Quine-McCluskey Method	QM	Tabular minimization, prime implicant charts, and algorithmic simplification
Multi-Level Circuits	MLEV	Multi-level gate implementations, bubble pushing, timing analysis, and circuit optimization
Combinational Modules	CMOD	Multiplexers, decoders, encoders, and standard combinational building blocks
Sequential Fundamentals	SEQF	Latches, flip-flops, timing parameters, and sequential logic basics
Sequential Design	SEQD	Registers, counters, FSMs, state machines, and sequential circuit design
Programmable Logic	PLD	ROM, PLA, PAL, CPLD, FPGA, and programmable device architectures
VHDL	VHDL	Hardware description language constructs, modeling styles, and simulation
System Integration	SYSI	Top-down design, datapath-controller partitioning, timing budgets, and system-level concepts

Category Descriptions

FOUND - Foundation Concepts

Core concepts that introduce the digital world, including the distinction between analog and digital systems, and fundamental terminology like bits, bytes, and words.

NUMSYS - Number Systems

The four primary number systems (decimal, binary, octal, hexadecimal) and their properties including positional notation and base concepts.

CONV - Number Conversions

All techniques for converting numbers between different bases, including direct conversion methods and shortcuts.

ARITH - Binary Arithmetic

Mathematical operations in binary including addition, subtraction, multiplication, division, and signed number representations (sign-magnitude, 1's complement, 2's complement).

BOOLF - Boolean Fundamentals

Introduction to Boolean algebra including variables, constants, truth values, and the three basic operations (AND, OR, NOT).

GATES - Logic Gates

Physical implementations of Boolean operations as electronic gates, including basic gates (AND, OR, NOT), derived gates (NAND, NOR, XOR, XNOR), and gate characteristics.

THEOR - Boolean Theorems

The mathematical laws and theorems of Boolean algebra including identity, null, idempotent, commutative, associative, distributive, absorption, and DeMorgan's theorems.

FORMS - Boolean Forms

Different ways to express Boolean functions including literals, product terms, sum terms, SOP, POS, and expression simplification.

COMB - Combinational Circuits

Design and analysis of combinational logic circuits, including specification-to-circuit translation and word problem conversion.

ACIR - Arithmetic Circuits

Specific circuit implementations for arithmetic operations including half/full adders, half/full subtractors, ripple carry adders, comparators, and parity circuits.

CANON - Canonical Forms

Minterms, maxterms, canonical SOP and POS forms, sigma and pi notation, don't care conditions, and function representations.

KMAP - Karnaugh Maps

K-map structure and techniques for visual simplification of Boolean expressions, including grouping rules, prime implicants, and optimization strategies.

QM - Quine-McCluskey Method

The tabular method for Boolean function minimization, including implicant tables, prime implicant charts, row/column dominance, Petrick's method, and computational complexity analysis.

MLEV - Multi-Level Gate Circuits

Design and analysis of multi-level logic circuits, including NAND/NOR implementations, bubble pushing, AOI/OAI gates, propagation delay, critical path analysis, and factoring techniques.

CMOD - Combinational Logic Modules

Standard combinational building blocks including multiplexers, decoders, encoders, priority encoders, demultiplexers, tri-state buffers, and bus architectures.

SEQF - Sequential Logic Fundamentals

Introduction to sequential logic including SR/D/JK/T latches and flip-flops, edge triggering, timing parameters (setup time, hold time, clock-to-Q delay), metastability, and timing diagrams.

SEQD - Sequential Circuit Design

Design of sequential circuits including registers, shift registers, counters, finite state machines (Moore/Mealy), state encoding, state minimization, and FSM design procedures.

PLD - Programmable Logic Devices

Programmable device architectures including ROM, PROM, PLA, PAL, CPLD, and FPGA. Covers programming technologies (fuse, antifuse, SRAM), CLBs, LUTs, and FPGA design flow.

VHDL - VHDL

IEEE 1076 hardware description language including entity/architecture structure, signal assignment, process statements, dataflow/structural/behavioral modeling, testbenches, and FSM implementation.

SYSI - System Integration

System-level design concepts including top-down methodology, hierarchical decomposition, datapath-controller partitioning, ASM charts, timing budgets, pipelining, verification, and UART protocol.