xnor-gate
The XNOR Gate: Champion of Equality in Digital Logic
TL;DR: The XNOR gate (Exclusive-NOR) outputs 1 only when its inputs are equal — both 0 or both 1. Boolean expression . Multi-input XNOR chains act as even-parity detectors, and...
xor-gate
The XOR Gate: Mastering the Logic of Difference
TL;DR: The XOR (Exclusive OR) gate outputs 1 only when its inputs differ. Boolean expression . XOR is binary addition modulo 2, the sum bit of a half adder, the...
karnaugh-maps
Karnaugh Maps: Visual Boolean Simplification
TL;DR: A Karnaugh map (K-map) arranges a truth table into a Gray-coded 2D grid where adjacent cells differ by one variable. Grouping adjacent 1s into rectangular powers-of-two produces minimal Sum-of-Products...
xor-gate
XOR vs. XNOR: The Critical Difference in Error Detection
TL;DR: XOR outputs 1 when inputs differ; XNOR outputs 1 when they match. Multi-input XOR chains detect odd parity; multi-input XNOR chains detect even parity. The choice between them depends...
digital-logic-101
Your First Circuits in DigiSim.io: A Beginner's Guide
TL;DR: This tutorial walks through three starter circuits in DigiSim.io: a switch-driven light (digital signals), a 2-input AND gate (logic gates and truth tables), and a multi-gate alarm system (combining...
arithmetic-circuits
Mastering Binary Addition: Building a 4-Bit Ripple Carry Adder
TL;DR: A 4-bit ripple carry adder chains four full adders so each stage's carry-out feeds the next stage's carry-in. The architecture is simple but slow: total propagation delay scales linearly...
shift-registers
Mastering Shift Registers: From Serial to Parallel Conversion
TL;DR: A shift register is a chain of D flip-flops where the output of each stage feeds the input of the next. On every clock edge, every bit shifts one...
truth-tables
Logic Gate Truth Tables: Your Essential Reference Guide
TL;DR: A truth table lists every possible input combination and the deterministic output a logic gate produces. This reference covers all seven standard gates — AND, OR, NOT, NAND, NOR,...
boolean-algebra
Mastering Sum of Products (SOP): Your Guide to Boolean Functions
TL;DR: Sum of Products (SOP) is a systematic way to turn any truth table into a Boolean expression: write one minterm for each row where the output is 1, then...
sr-latch
The SR Latch: The Simplest Digital Memory Element
TL;DR: The SR (Set-Reset) latch is a bistable circuit built from two cross-coupled NOR gates (active-high) or two cross-coupled NAND gates (active-low). It supports Set, Reset, and Hold operations but...
information-theory
Maxwell's Demon: The Physical Cost of Information
TL;DR: Maxwell's Demon was a 19th-century thought experiment that seemed to violate the Second Law of Thermodynamics by sorting molecules without doing work. Landauer's Principle resolved the paradox: erasing one...
binary
The 3,500-Year Journey of Binary, From Ancient Egypt to Now
TL;DR: Binary representation predates the computer by 3,500 years. Egyptian scribes used a shift-and-add multiplication algorithm, the I Ching encoded a 6-bit cosmology, and Pingala's Chandaḥśāstra gave the first explicit...
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