Plain-language explanations of how the things behind our tools work.
How a name becomes an IP address through resolvers, root, TLD and authoritative servers, the record types, TTL and caching, and DNS security basics.
How an IP address splits into network and host parts, how to find a network and broadcast address, divide a /24 into four /26s and size a subnet.
Title, description, canonical, hreflang, robots.txt, Open Graph and JSON-LD explained with real generated examples and the mistakes that cost rankings.
The seven parts of a URL, which characters need percent-encoding and why, how query strings carry repeated keys, and how international domain names become punycode.
What SPF, DKIM and DMARC each check, what their DNS records look like, how alignment works and a safe order for rolling them out to stop spoofing.
How mail servers encrypt delivery between each other: STARTTLS and why it can be downgraded, what MTA-STS and TLS-RPT add, the exact DNS records and policy file, and how this differs from SPF, DKIM and DMARC.
What a hash function does, the avalanche effect shown with real SHA-256 output, which algorithms are still safe, HMAC, and how to store passwords properly.
How the TLS 1.3 handshake, key exchange and certificate chain make a connection private and authenticated, what the padlock does not prove and why certificates fail.
The three parts of a JWT with a real decoded example, the registered claims, how servers verify the signature, HS256 versus RS256 and the pitfalls to avoid.
How the six-digit codes in an authenticator app are derived from a shared secret and the clock, with a verified RFC test vector, plus their limits against phishing.
UTC, offsets and time zones, daylight saving, Unix time and the 2038 problem, leap years, week numbers and day counts, with every example run in code.
How computers store decimals as a sign, exponent and fraction (IEEE 754), why 0.1 is not exact, what rounding, subnormals, infinity and NaN are, and how to compare and add floats safely.
The six JSON value types, why parsing fails, traps with big integers and key order, JSONPath queries and converting JSON to TypeScript, TSV and more.
How words and reading time are counted, Flesch readability, naming-case styles, line diffs, sorting, de-duplication and escaping for JSON, regex and SQL.
Code points, planes and encodings explained: how UTF-8 stores characters in 1 to 4 bytes (with a verified table), what UTF-16 surrogate pairs are, why é can be one or two code points, and how to avoid mojibake.
The structure of a UUID (version and variant bits), what each version means, why random UUIDs almost never collide (with the birthday-paradox numbers) and how to generate and decode them.
What encoding is (and is not), how Base64 turns three bytes into four characters, why it adds a third, and the mistakes to avoid.
Place value in binary, octal and hexadecimal, converting 202 between all of them step by step, hex colours, bit operations and two's complement.
The structure of a PDF (header, objects, cross-reference table, trailer), a complete minimal file whose offsets were checked with pdfinfo, how pages and text are stored and how editing leaves traces.
Hex, RGB and HSL are one colour, how the WCAG contrast ratio is computed with real pass and fail examples, colour-blindness and building accessible palettes.
JPEG, PNG, GIF, WebP, AVIF, HEIC and SVG compared with measured file sizes, lossy versus lossless, aspect ratio and print maths, and which tool to use.
QR versions and sizes, the four error-correction levels, exact capacity limits, and how UPC and EAN check digits are computed, verified with the real libraries.
Bayes' theorem explained with natural frequencies: how a 90 % accurate test with a 1 % base rate gives only a 9 % chance of disease, how likelihood ratios update beliefs, and where it goes wrong.
Pseudo-random versus secure randomness, modulo bias, why naive shuffles are biased, streaks, exact lottery, dice and Secret Santa odds and fair brackets.
What standard deviation measures, a worked step-by-step example, why samples divide by n − 1, the 68-95-99.7 rule, z-scores and how spread becomes uncertainty.
Why decibels use a logarithm, the 10 and 20 formulas for power and voltage, the rules of thumb (3 dB, 6 dB, 10 dB), how to add sound levels and how level falls with distance, with a table checked in code.
Voltage, current and resistance, Ohm's law, the power formulas, series and parallel resistors and voltage dividers, explained with worked examples.
The compound interest formula with a worked $10,000 example, how compounding frequency matters, APR versus APY, the Rule of 72 and the effect of regular saving.
Avalanche versus snowball on one worked example with real totals, why minimum payments take so long, and when consolidating a debt actually helps.
Auto, personal, student, business, mortgage, HELOC, lease and reverse-mortgage loans compared, with Canadian compounding, points break-even and factor rates worked out.
ROI, annualised return (CAGR), IRR, NPV and payback period explained with one worked example, and why a plain average of yearly returns misleads.
The loan payment formula, why early payments are mostly interest, a worked $200,000 example month by month, and how extra payments shorten the loan and save interest.
Gross to net pay, marginal versus effective tax rates built slice by slice, self-employment tax, freelance rates, raises, commissions, budgets and unit prices.
Regular saving, employer match, fees and inflation, traditional versus Roth, the 25x rule and 4% withdrawal test, annuities, pensions and RMDs, all computed.
BMI, waist-to-height ratio, waist-to-hip ratio, relative fat mass and body roundness index compared: the formulas, a worked example for one person, what each captures and where each misleads.
BMR, TDEE and calorie targets explained with one worked example: three BMR equations, activity factors, the 7,700 kcal rule, macros and energy out.
The 280-day rule from the last period, conception, IVF and ultrasound dating, ovulation and fertile days, hCG doubling and weight-gain guidelines, with dates computed.
What EXIF stores inside a photo, where it sits in a JPEG, how to turn GPS degrees into decimal coordinates, why it is a privacy risk and how to remove it.
How the first bytes of a file identify its real type, a table of common signatures verified against real files, why extensions can lie and where signatures matter.