binary arithmetic

Christopher Domas's REcon 2013 talk on dynamic binary visualization for reverse engineering. He shows how rendering binary data as interactive visual maps and trigraphs reveals structure that hex dumps hide, leading to his Cantor.dust tool.

Christopher Domas presents his Cantor Dust tool at Derbycon 2012, a 3D visual approach to reverse engineering binaries by visualizing their structure dynamically.

A 1969 BBC Tomorrow's World segment about Nellie, a school computer used by pupils at Forest Grammar School to solve equations and play music. Students learn programming and maintenance, and act out binary arithmetic.

John Gustafson presents posits, a proposed drop-in replacement for IEEE 754 floats that is simpler in hardware and more flexible in precision. The seminar includes a live demo and machine learning results.

A 95-minute recorded debate at the ARITH23 computer arithmetic conference between John Gustafson, proponent of unums/posits, and William Kahan, architect of IEEE 754 floating point. They argue the merits of the new number formats versus conventional floats and interval arithmetic.

Physicist Al Bartlett's well-known lecture on the arithmetic of exponential growth, applied to population, energy consumption and resource depletion. He argues that steady percentage growth cannot be sustained on a finite planet and that most public discussion ignores this.

A recording of physicist Albert Bartlett's well-known lecture on the arithmetic of exponential growth, applied to population and energy use. He argues that steady percentage growth in a finite world cannot continue and sneaks up suddenly.

Andrew Kelley's Zig SHOWTIME talk on an experiment to ship static Linux executables that can do graphics and gaming, followed by an interview. It covers the problems of Linux binary stability, dynamic linking and the graphics ABI.

Numberphile with Daniel Erman on the Josephus problem, where people in a circle are eliminated in turn. It shows how the survivor's position follows a neat pattern tied to powers of two and binary.

Matt Parker of Stand-up Maths explains why people keep making the same mistake with millions and billions, using a Bloomberg cash calculator example. He looks at the unit slip behind the repeated arithmetic error.

Matthias Wandel shows his wooden machine that adds binary numbers using marbles. It demonstrates computation with purely mechanical logic.

3Blue1Brown explains why plotting primes in polar coordinates produces spiral patterns, using modular arithmetic, Dirichlet's theorem and rational approximations of pi.

Khalil Estell's CppCon 2024 talk argues C++ exceptions can reduce binary size in firmware. He digs into how exceptions work and how to shrink their code footprint on embedded platforms.

Casey Muratori follows up his refterm proof-of-concept, a GPU-based terminal renderer, with a second part covering memory usage, glyph sizing and correct Unicode and VT handling. It is built to show that a terminal can be fast and correct without heroic effort.

MinutePhysics explains Shor's algorithm, showing how a quantum computer factors large integers by finding the period of a number modulo N. It walks through the modular arithmetic and number theory that give the exponential speedup over classical factoring, and why this threatens encryption.

Physicist Albert Bartlett's full-length lecture on how steady exponential growth in population and energy use collides with finite resources. It uses examples like bacteria in a bottle and covers peak oil.

Tom Scott explains for Computerphile how floating point numbers work, why moving the binary point is fast, and why it handles money badly.

Numberphile's James Grime makes the case for base 12 (dozenal) over base 10, showing how twelve's many divisors make arithmetic and everyday fractions easier.

A 72-minute Q&A with Linus Torvalds at DebConf 14. Topics include the pain of distributing Linux binaries, distro fragmentation, kernel backwards compatibility, GPLv2 versus GPLv3 and conduct.

Mathologer shows how times table diagrams on a circle produce cardioids and other curves connected to the Mandelbrot set. He explains the patterns and links to a tool for making your own diagrams.

Rusty Russell and Matt Evans examine why Unix utilities like ls and cat grew from a few kilobytes to over a hundred kilobytes. They take apart common tools to see where the growth comes from.

Bill Dally of NVIDIA gives a University of Washington lecture on trends in deep learning hardware. It covers numeric formats, specialized instructions, energy per operation and co-design of hardware and software.

Tom Scott-style absurdist tour by Tom7 of SIGBOVIK chess projects: a tournament of 30 weird chess algorithms used to rate a color- and piece-blind chess program. Topics include mirrors, arithmetic encoding, perverted game tree search and a diluted Stockfish.

jan Misali presents an humorous but earnest case for counting in base 6 (seximal) instead of base 10 or 12, comparing the arithmetic advantages of each.

Matt Parker explains the history behind NTSC television running at 29.97 frames per second rather than 30, tracing it to the backward-compatible addition of color. He walks through the arithmetic behind the odd ratio.

David MacKay's TEDxWarwick talk uses basic arithmetic to show how much land and energy renewables would need to power a country like the UK. It explains the limits of sustainable options and why they should still be pursued.

Aditya Siram introduces ATS, a statically typed ML-like language that compiles to C and offers type-safe pointer arithmetic and a full proof language. The Strange Loop talk shows off C interop, concurrency and verification features with non-trivial examples.

Christof Paar's university lecture introducing Galois fields and finite-field arithmetic as used in AES. It covers the mathematics behind the AES S-box.

A short CGP Grey animation showing how the US electoral college lets a candidate win the presidency with as little as about 22 percent of the popular vote. It lays out the arithmetic of winning states by narrow margins.

Vladimir Voevodsky's IAS lecture starts from Godel's second incompleteness theorem to explore whether first-order arithmetic could be inconsistent. It motivates his vision of univalent foundations and computer-checked proofs.

A reverse engineer walks through fixing a ten-year-old bug in Guitar Hero III without access to its source code, using a disassembler and decompiler. It is technical but explained step by step.

A short Art of the Problem clip explaining Diffie-Hellman key exchange, using a paint mixing analogy for one-way functions and touching on modular arithmetic and discrete logarithms.

Matt Parker of Stand-up Maths explains single-pile Nim and the trick that wins it, using Dr NIM, a 1960s mechanical plastic computer that plays perfectly. He teaches the strategy so viewers can beat friends.

A 256-byte MS-DOS intro that renders a raymarched, procedural 3D animation. It won the 256-byte competition at Riverwash 2009 and the scene.org award for best technical achievement that year, and the author published commented x86 assembly source.

Gernot Heiser presents seL4, a microkernel with a mathematical proof connecting security properties to the binary code, and explains what its open-sourcing means for users. It covers its roles as a microkernel, separation kernel and hypervisor.

OpenAI cofounder Greg Brockman explains the design principles behind ChatGPT and demos unreleased plug-ins at TED 2023. In the follow-up, TED head Chris Anderson presses him on the timeline of development and the risks of releasing such a tool.

A London Haskell talk on the algebra of algebraic data types, showing how sum and product types behave like arithmetic. It frames types as numbers obeying algebraic laws.

Rob Miles discusses GPT-3 on Computerphile, covering how scaling parameters kept improving results over GPT-2 and how the model nearly learned arithmetic without anyone knowing exactly how.