Logic gates—digital versions of conditional statements, such as 'if 0 and 1, then 1'—are specialized circuits that combine multiple digital signals, like the binary code representing numbers, into a single output, thereby allowing machines to perform math.

An explanation of Turing machines—the foundations of digital algorithms and computers

The device reads data, overwrites or ignores it, and then moves on to the next piece of data based on a set of programmed rules. By imagining this data as zeros and ones—binary that makes up computer code—Turing machines became the theoretical models for how any algorithm could be run on a computer if the procedure could be coded into a set of digital rules.

Transistors are the foundational components of integrated circuits and microchips and manage the processing of electronic signals by controlling the flow of electricity.

The Model K—named for its construction on a kitchen table—was the first electromechanical digital binary adder, which used an electric circuit to provide the sum of a pair of zeroes and ones in binary.

Before transistors, which regulate the flow of electricity, vacuum tubes—glass tubes containing no gas that resemble light bulbs—served as the electronic switches in computers.

Integrated circuits come in digital, analog, or mixed types

Each type can be further divided based on application, technology, and integration level. Digital ICs are used in computer memories and microprocessors, while analog ICs process continuous signals within sensors, including temperature, light, and sound.

With many smaller computing cores, graphics processing units process many identical tasks in parallel, whereas central processing units have fewer, larger cores built to handle a wide variety of more complex tasks sequentially.

Transistors in traditional computers are physically limited to atomic scales

As computer parts shrink, transistors—tiny switches that control the path of electrical signals—become obsolete because electrons can quantum tunnel through switch barriers. This makes quantum computers, which take advantage of quantum effects, an enticing alternative.

All computers are defined by their ability to input, store, process, and output data

From wooden machines to wearable tech, computers have changed a lot in appearance, but they all still perform the same essential tasks. Early computers were made of wood and metal—some were so big that they filled entire rooms just to solve simple math problems.

Turing machines consist of an infinite tape, a read-write mechanism and instructions

Based on the information the mechanism reads on the tape, the machine follows the applicable instruction (e.g., if you read a 1, write a 0) and may proceed to the next cell of data. Given enough time and memory, Alan Turing proposed such a machine could perform any computation.

A simple explanation of semiconductors

Semiconductor chips are electronic devices that store and process information. Today they can contain billions of microscopic switches on a chip smaller than a fingernail. The article provides a quick overview of how the devices work and how they've provided the backbone of the computer age.

Semiconductor chips are electronic devices that store and process information

They can contain billions of microscopic switches on a chip smaller than a fingernail. An article provides a quick overview of how the devices work and how they’ve provided the backbone of the computer age.

A breakdown of algorithms, how they are constructed, and their applications

Algorithms are instructions for accomplishing a goal and typically take the form of a step-by-step procedure. Given the conditions, these procedures can take various paths, increasing an algorithm's complexity. While traditional computer algorithms are programmed to account for all possible scenarios within a given process, machine learning systems build their own rules from data-driven patterns.

Logic bomb viruses can awaken from a dormant phase without human input

Theoretically, computer viruses can remain idle indefinitely while awaiting specific user actions, as instructed by their code. However, logic bombs—embedded code that triggers when specific conditions are met—can automatically execute viruses, such as when a certain date or time is reached.

The work of Claude Shannon, for whom Anthropic's AI chatbot is named

Known as the father of information theory, Claude Shannon applied Boolean algebra—a subset of mathematics that quantifies true or false statements as 1 or 0, respectively—to circuit design to develop the concept of a binary digit. His paper "A Mathematical Theory of Communication" (1948) laid the groundwork for all modern digital systems.

More than 2,000 years ago, a hand-powered model of the solar system called the Antikythera mechanism—the oldest example of an analog computer—could predict solar eclipses.

See how computer memory really works—from binary bits to modern RAM

The video explains how computers store information as 1s and 0s, how RAM functions as fast working memory, and why systems utilize different types of storage. The video demonstrates how this process enables computers to operate.

The first compiler to facilitate communication with computers was developed by Grace Hopper

The A-0 program linker automatically translated mathematical symbols into machine-readable binary code. Although it took two years for computer executives to get on board with the idea, the technology was foundational to future programming languages that allowed computers to understand commands written in word-based languages.

Quantum computers harness weird physics to explore unsolvable problems

Classical computers manipulate bits as either 0 or 1, but quantum computers use qubits to hold combinations of both, enabling new algorithms. This new approach could one day help with breakthroughs in medicine, chemistry, and AI.

An overview of 12 fundamental types of algorithms and the uses for each

These include search algorithms to quickly process and find important information, cryptographic algorithms to secure communications, randomized algorithms—such as Monte Carlo simulations for estimating probabilities of outcomes—and greedy algorithms, which make optimal choices based on available data in a step-by-step fashion, as seen in navigation apps.

Quantum computers use qubits to solve problems much faster than classical machines

Unlike regular computers, where each bit is either 0 or 1, quantum computers use qubits, which can simultaneously be both—allowing for massive parallel processing power. Google’s quantum processor once solved a problem in seconds that would have taken a supercomputer 47 years.

Lasers help build the layers of circuit components in microchips

During the photolithography process, light is projected through a blueprint onto a light-sensitive chemical layer on silicon wafers, etching patterns that become transistors through a series of successive reactions. These processes require significant electricity, as only about 2% of photons reach the wafer.

There is a limit to how small transistors can become because they rely on being able to allow or block the flow of electrons, but quantum effects allow electrons to leak through these barriers, generating heat, current loss, and potential data errors.

Take a virtual tour inside the NVIDIA GA102 graphics processing unit to explore the architecture that enables it to perform over 35 trillion calculations per second.

Qubits let quantum computers process massive datasets all at once

The quantum phenomena of superposition and entanglement enable qubits to act in 0 and 1 binary states simultaneously and influence each other instantly. These features give quantum computers incredible power, though keeping them stable is a major challenge.

As of 2025, the College Board has banned the use of calculators with computer algebra systems on the SAT and PSAT.

Lasers, semiconductors, medical imaging, and atomic clocks rely on quantum mechanics

Semiconductors, crucial in electronics, operate based on quantum superposition. Lasers use stimulated emission, a quantum process, and MRI machines leverage the quantum spin of hydrogen atoms for imaging. Atomic clocks measure time with unprecedented precision using quantum transitions.

An integrated circuit combines major circuit components onto a single device

Before 1958, these components were fabricated separately before manual assembly, introducing human error, delays, and higher costs. The invention of the IC laid the foundation for automated manufacturing, miniaturization, and improvements to speed and energy efficiency.

Slide rules—ruler-sized mechanical calculators with a component that slides out to show relationships between numbers—were used by engineers at NASA during the Apollo missions.

Quantum computers can simulate nature more effectively than classical computers

Ordinary computers struggle to simulate quantum fields due to entanglement, but systems built from those elements can model the complexity. Systems using particle in more than two states—qudits—have successfully modeled 2D electromagnetic fields and done so more efficiently.

Computational and biological systems share fundamental principles, like randomness

Proposed by Alan Turing and John von Neumann, the concept originates from how DNA and computers run by executing encoded instructions in parallel. The advent of AI and the temperature parameter has seen neural networks mimic the randomness of protein encoding.

English mathematician Ada Lovelace wrote the first computer algorithm a century before computers existed and hypothesized that computing devices would one day be able to compose music—foreseeing the generative AI systems of today.

How quantum computers can empower Shor's algorithm to break digital encryption

Secure communications largely rely on numeric keys generated by multiplying two enormous prime numbers together, and it is computationally impractical to determine these primes by trying to divide by every possible one. While Shor's algorithm can provide better guesses for this brute-force approach, it relies on a number that is difficult to determine on classical computers but much easier to calculate using the simultaneous computations enabled by quantum superposition.

Photonic integrated circuits use light instead of electrons within circuit components

Instead of processing electric signals, photons in the visible and near-infrared serve as optical signals between chips made of electro-optical crystals. PICs can enable lower power consumption and heat generation by eliminating the friction from electrons moving along wires.

Graphics processing units, which process large amounts of data in parallel, have become the foundational hardware for AI systems that rely on hardware capable of processing millions of text parameters simultaneously.

Calculators convert input values into a form of scientific notation—a fixed set of digits with a decimal multiplied by a base to some exponent—to store and process very large or very small quantities efficiently at the cost of rounding errors.

Misunderstandings about how quantum computing works may have overhyped their ability

Quantum computers are often viewed as machines that can solve all problems instantly by trying every solution simultaneously. Instead, they amplify correct answers and cancel out wrong ones, which only works for specific kinds of problems with special structures.

Explore interactive simulations of strange attractors, the graphs that help visualize chaos

Although simple, linear equations reach an explicit value for a given input, such as *f(x) \= x* + 1 equaling 4 when *x* equals 3, some chaotic, nonlinear systems tend to evolve towards multiple values simultaneously. These simulations allow users to observe the unusual mathematical artifacts created by systems as their outputs evolve toward these distinct values.

The internet explained at five levels of difficulty, from protocols to internet flattening

Resembling a roadway with traffic laws that all cars must follow, the internet is the hardware that connects a source to a destination, and these connections must follow specific software rules. Although data had to travel through about 10 networks to reach a destination in the past, data centers increasingly consolidate traffic, just as a highway does for cars, to improve data speeds.

Since computers rely on the distribution of electrons in microchips to represent binary code, cosmic rays and ionizing radiation from radioactive elements can introduce software errors by detaching electrons from atoms.

COBOL was partly derived from Grace Hopper's FLOW-MATIC programming language

The Common Business-Oriented Language was developed for business data processing, supporting precise decimal calculations and an English-like syntax. Able to work across operating systems and hardware environments, COBOL and its newer versions support 80% of in-person credit card transactions and 95% of all ATM transactions.

One of the first mechanical calculators—the Pascaline—was built in the 1640s by French mathematician Blaise Pascal to help his father, who worked as a tax collector.

Neurons send signals through electrical impulses and chemical messengers

By converting electrical signals into chemical messages at synapses, neurons allow information to travel throughout the nervous system. With repeated use, synapses grow stronger, enhancing the associations between neurons.

Within fabrication plants, it takes about three months to manufacture hundreds of microchips from a single wafer of pure silicon using light and significant quantities of electricity, water, and hazardous chemicals.

With a core consisting of a glass fiber roughly the width of human hair, fiber-optic cables transmit digital information via flashes of light that reflect within the glass.

FLOW-MATIC was the first programming language resembling the English language

As part of the team working on UNIVAC—the first commercially produced electronic digital computer in the US—Grace Hopper helped develop the system that enabled nonprogrammers and businesspeople without a strong mathematics background to use the machine effectively, thereby enhancing the computer's commercial viability.

The history of graphics processing units began with hardware for displaying visuals in arcade machines, but the transition to 3D graphics led to the microchips and software that power today's AI data centers.

Create your own cipher by combining mathematical operations and encryption protocols

This tool allows users to build an encryption workflow in which the output of one customizable function becomes the input to another, thereby creating undiscovered methods for obscuring information via a series of ciphers.

DNA computing allows for storage and processing of massive amounts of data

Although costly and less efficient for simpler tasks, as of 2025, DNA could hold 455 exabytes of data with near limitless parallel computation potential in small data centers. Every movie ever made would fit inside the volume of a single sugar cube.

Moore's Law came from observing exponential computing growth in the 1960s

In 1965, Gordon Moore, cofounder of Intel Corporation, observed a four-year trend of constant growth rate in computing power. Hypothesizing the trend would continue, his observation became the benchmark that the computing industry has worked to maintain for 60 years.

A simple visual explanation of how blockchains work

Blockchains are decentralized, distributed, and digital methods to record transactions and prevent alterations and tampering of the record. That's a simplified definition. This easy-to-understand six-minute video further and better explains what blockchains are and how they work using colorful illustrations and clear, concise clarifications on their processes and what makes them so special.