How Binary Converters Work and Why They Matter

Welcome

Binary converters might sound like a techie-only topic, but they play a key role even in everyday devices. Whether you're working with stock trading platforms, financial analysis software, or teaching concepts of computing, understanding how binary converters work is quite useful.

At its core, a binary converter switches numbers between binary—just zeros and ones—and other number systems like decimal or hexadecimal. This translation is essential because computers think in binary, but humans are more comfortable with decimal numbers.

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Without binary converters, digital technology like smartphones, trading algorithms, or interactive educational tools wouldn't function properly.

In this article, we'll walk through the basics of binary code, look at how conversion methods work, and explore where these converters pop up in real-life scenarios. By the end, you’ll see why binary converters matter—not just as abstract concepts but as practical tools influencing everyday computing and electronic devices.

Whether you're an investor trying to grasp how data flows through your trading systems, or an educator simplifying digital tech to your class, this overview will bring you closer to the heart of digital communication.

Basics of Binary Code

To get a solid grip on binary converters, you first gotta understand the basics of binary code. It forms the backbone of how computers and digital tech communicate. Without knowing what binary is, all the converting in the world wouldn’t make much sense. We use binary to represent every type of digital data — from your morning stock portfolio updates to complex financial transactions happening in milliseconds across global markets.

What Is Binary?

Definition and significance

At its core, binary is a way of counting using only two symbols: 0 and 1. This contrasts with the decimal system we're used to, which counts in tens (0 through 9). Binary's simplicity is why computers use it — electronic circuits easily recognize two states: on or off, which map perfectly to 1 and 0. This isn’t just theory; it’s how your trading apps, brokerage software, and financial databases store and process information.

Binary digits (bits)

Each symbol in binary is called a bit — short for "binary digit." Think of bits as the smallest units of data in computing. Just like how money piles up one shilling at a time, data builds bit by bit. For example, eight bits make up a byte, which is common in storing a letter or a small number. Understanding bits helps you appreciate the foundation of digital data flow in platforms that you rely on daily.

Representation of information

Binary isn’t just for numbers; it represents all sorts of info by listing different patterns of 0s and 1s. Letters, images, even sound waves get converted into binary code. Imagine your favorite financial reading app showing graphs — under the hood, it’s all these bits working in harmony to produce that crisp you see on your screen.

Binary Number System Compared to Decimal

Base differences

The decimal system counts in base 10, meaning each place value represents powers of 10 (like 10, 100, 1000). Binary, however, uses base 2 — every position stands for a power of 2 (1, 2, 4, 8, and so on). This fundamental difference changes how numbers are built and understood.

How binary counts

Binary counting starts simply: 0, 1, then it rolls over to 10 (which equals decimal 2), 11 (decimal 3), and so forth. Each new digit added doubles the highest number you can represent. So, while decimal has 10 digits per position, binary only has 2, but the logic stacks quickly.

Examples of both systems

To make this clear, consider the decimal number 13. In binary, it’s written as 1101. Here’s why:

• The rightmost bit represents 1 (2^0), which is 1.

• Next bit left is 0 (2^1), so 0.

• Then 1 (2^2), which equals 4.

• The leftmost 1 is 2^3, or 8.

Adding these: 8 + 0 + 4 + 1 = 13.

If you flip those digits back, seeing the binary version helps demystify how data is stored and manipulated in digital systems — knowledge crucial if you deal with trading platforms, where every bit can influence how algorithms read data.

Grasping the basics of binary code isn’t just academic — it’s essential for anyone interacting with digital tech daily. Whether you run financial models or handle trading systems, understanding these fundamentals sharpens your edge.

Understanding binaries lays the proper groundwork to appreciate how binary converters operate, which we'll dive into next! This isn’t just geek talk; it’s about seeing how the digital world ticks behind the scenes.

What Is a Binary Converter?

At its core, a binary converter is a tool or device that changes numbers between the binary system and other numbering systems, mainly decimal. This process is essential because computers operate with binary code—strings of 0s and 1s—while humans tend to use decimal numbers in daily life. So, a binary converter helps bridge the gap between human-friendly numbers and machine-readable code.

Why does this matter? Well, without the ability to convert between these formats, programming, data processing, and even interpretation of digital signals would be confusing or outright impossible. Think of it like translating between two languages: without a translator, communication stops.

Beyond just a simple utility, binary converters have a variety of practical benefits:

• Enabling programmers to check the binary equivalents of instructions or numbers.

• Assisting hardware engineers in debugging microcontroller inputs or outputs.

• Helping educators teach the foundational understanding of digital systems.

For example, when you input a decimal number like 27 into a software that controls an LED display, the system needs to convert that number into binary (11011) to light the appropriate segments. That’s where binary converters step in — silently doing the behind-the-scenes work needed for digital tech to function smoothly.

Purpose of a Binary Converter

Converting binary to decimal:

This process turns a sequence of binary digits into a more common decimal number. It's essential because most people find decimal easier to understand and use. For instance, a financial analyst who comes across a raw binary series representing a value could use a converter to translate it into decimal before running computations or making sense of the data.

Imagine getting a transaction code in binary form; without converting, it’s just an unreadable string. The binary-to-decimal converter makes those figures clear and actionable.

Converting decimal to binary:

This direction is just as important. Computers read data in binary, so when programmers or traders input decimal numbers—say, stock quantities or pricing thresholds—they must be converted into binary commands that the digital system understands. This conversion also underpins various computing tasks, like setting flags or configuring hardware components.

For example, entering the decimal number 45 for some automated trading parameter requires its binary equivalent, 101101, to be loaded properly.

Other conversions involving binary:

Besides just decimals, binary converters handle changes between binary and other systems like octal or hexadecimal. These are often used in computing because they condense binary strings into fewer digits, making complex data easier to read and manage. Hexadecimal, for example, is popular in programming to represent memory addresses or colors in a compact form.

This flexibility to convert binary data across multiple formats makes the binary converter an indispensable part of digital workflows.

Types of Binary Converters

Manual methods (e.g., division by ):

Before digital tools took over, people converted numbers manually. One common method to turn decimals into binary is by repeatedly dividing the decimal number by 2 and noting the remainders. While time-consuming, this method strengthens understanding of how binary works.

For example, converting 13 to binary manually involves:

1. 13 ÷ 2 = 6 remainder 1

2. 6 ÷ 2 = 3 remainder 0

3. 3 ÷ 2 = 1 remainder 1

4. 1 ÷ 2 = 0 remainder 1

Reading remainders from bottom to top gives 1101, the binary equivalent.

Digital tools and software:

Nowadays, software like Windows Calculator or online converters can process these changes instantly. These tools usually support multiple formats and can handle large numbers, relieving users from manual errors and saving time.

Traders or analysts who handle large datasets or need quick conversions can rely on such tools to boost efficiency and accuracy.

Hardware converters:

In electronics, hardware binary converters are built circuits that translate between binary and other signals automatically—in real time. Microcontrollers inside gadgets, for instance, often include hardware circuitries that convert inputs from sensors (in analog or decimal-like signals) to binary data for processing.

This hardware-level conversion is critical since it allows digital devices to interact with the physical world swiftly without extra manual steps.

By understanding what binary converters are, what they do, and the types available, you can better appreciate their role in digital technology, especially in finance and tech sectors where precise data handling is a must.

How Binary Converters Work

Understanding how binary converters operate is key to seeing their role in technology and everyday computing. These converters serve as the bridge translating numbers between human-friendly decimal systems and machine-friendly binary code. Without this translation, computers and digital devices would struggle to correctly interpret or process data.

Binary converters work on clear, logical processes, often driven by straightforward algorithms. These involve breaking down numbers and reconstructing them in binary or decimal formats depending on the conversion direction. Grasping these steps helps financial analysts and traders appreciate the digital backbone behind software tools and platforms they use daily.

Step-by-step Conversion Processes

Decimal to binary conversion steps

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Converting decimal numbers to binary might seem tricky at first, but it breaks down into manageable steps anyone can follow. You start by dividing the decimal number by 2, noting the remainder each time—this remainder is either 0 or 1, representing a binary digit (bit). You repeat the division with the quotient until it reaches zero. The binary number is then built by reading all the remainders in reverse order.

For example, converting the decimal number 19 to binary:

• 19 divided by 2 is 9 with a remainder of 1

• 9 divided by 2 is 4 with a remainder of 1

• 4 divided by 2 is 2 with a remainder of 0

• 2 divided by 2 is 1 with a remainder of 0

• 1 divided by 2 is 0 with a remainder of 1 Reading the remainders backward gives 10011—which is 19 in binary.

This method shines in both simple hand calculations and programming scripts, letting users easily move from decimal to binary when needed.

Binary to decimal conversion steps

Shifting from binary back to decimal involves interpreting each bit according to its position, based on powers of 2. You multiply each bit by 2 raised to the position’s power, starting from zero on the right, then sum them all.

Take binary 10110 as an example:

• The rightmost bit (0) × 2^0 = 0

• Next bit (1) × 2^1 = 2

• Next bit (1) × 2^2 = 4

• Next bit (0) × 2^3 = 0

• Leftmost bit (1) × 2^4 = 16 Add them up: 16 + 0 + 4 + 2 + 0 = 22 in decimal.

This step-by-step approach helps traders and programmers verify conversions quickly without relying solely on software.

Common Conversion Algorithms

Division-remainder method

This is the classic approach for decimal to binary conversion just described. It’s reliable and straightforward, making it ideal for manual calculations and simple programs. Its strength lies in clear logic — breaking a number into bits bit by bit.

Subtraction method

The subtraction method works by determining the largest power of two less than or equal to the decimal number, subtracting it, and marking a '1' in the corresponding binary place. The process repeats with the remainder until it reaches zero, filling in '0's where powers don’t fit. This method feels a bit like fitting puzzle pieces neatly and is beneficial when mental math or estimation is needed.

For instance, to convert 13:

• Largest power ≤ 13 is 8 (2^3), subtract 8 → remainder 5, place '1' in 2^3

• Largest power ≤ 5 is 4 (2^2), subtract 4 → remainder 1, place '1' in 2^2

• Largest power ≤ 1 is 1 (2^0), subtract 1 → remainder 0, place '1' in 2^0

• Place '0's in unused spots (2^1 → 0) Final binary: 1101.

Using positional values

Using positional values is particularly helpful in binary to decimal conversions. Each position has a weight (2^position), and the sum of weights where bits are '1' equals the decimal number. This method encourages a deeper understanding of the number system, reinforcing concepts valuable for anyone working with data encoding or programming low-level calculations.

Being comfortable with these methods arms professionals with skills to cross-check binary-related data quickly, a handy advantage in data-heavy environments like finance or education.

Overall, knowing how binary converters work, through these practical steps and algorithms, unlocks a clearer perspective of computing fundamentals. This knowledge supports informed use of technology and problem-solving approaches when digital systems behave unexpectedly.

Online Binary Conversion Tools

Online binary conversion tools have become go-to resources for anyone dealing with binary numbers—from students to seasoned financial analysts needing quick conversions. Their relevance grows as digital communication and computing become more embedded in our daily work. These tools simplify what used to be a time-consuming manual process by instantly converting between binary and decimal systems, hexadecimals, and other numeral systems.

Popular Websites and Software

Features of Common Converters

Popular online converters like RapidTables, BinaryHexConverter, and Omni Calculator share several practical features. They typically provide an intuitive user interface where you enter the decimal or binary values, then instantly get the converted result. Many support not just binary-decimal conversions but also extend to octal and hexadecimal, which is handy for traders dealing with technical analysis tools powered by digital systems. Some advanced converters offer batch processing, letting users convert lists of numbers at once, trimming down repetitive tasks efficiently.

Advantages of Using Online Tools

The standout advantage is speed and convenience. Rather than pulling out a calculator or going through manual steps, online converters deliver instant outputs, saving valuable time during fast-paced trading or research. They also minimize human errors linked to place value misunderstandings. Another perk is accessibility; you can use these tools from any device with internet access, whether at home, in an office, or on the move. For educators, such resources become great teaching aids, offering students practical experience without needing to slog through complex calculations on paper.

Limitations of Online Converters

Accuracy Issues

While most reputable online converters are accurate, especially the popular ones mentioned earlier, occasional glitches can happen—particularly if the input format isn’t standardized or gets misinterpreted. For instance, entering a binary number without proper spacing or leading zeros might throw off the result. It’s wise to double-check conversions, especially when they feed into critical financial models or data analytics. Also, some converters might not handle extremely large numbers correctly, so relying solely on them without verification can lead to costly mistakes.

Data Privacy Concerns

Since many online converters are free and web-based, users should be cautious about entering sensitive or proprietary numeric data. Most of these tools do not store user inputs, but not all sites are transparent about their privacy policies. For financial analysts handling confidential codes or proprietary system outputs, it’s safer to use offline tools or verified software like Microsoft Power BI or MATLAB with built-in conversion functions. Always consider the sensitivity of your data before using any online service to avoid unintended leaks.

When speed matters, online binary converters are a handy option, but they’re best paired with validation checks and security awareness.

In sum, online binary conversion tools offer tangible benefits by simplifying number system translations, but professionals must weigh convenience against potential accuracy and privacy pitfalls.

Applications of Binary Converters in Daily Life

Binary converters aren’t just abstract tools used by engineers and programmers; they have practical roles that touch on many daily technologies. Understanding how binary converters function can reveal a lot about the devices and systems we interact with every day. From the smartphone in your hand to the traffic lights on the roads, binary conversion forms the backbone of digital operations.

Use in Computing and Programming

Data processing

At the heart of data processing lies the binary converter. Computers fundamentally operate with binary data because it’s the simplest way to represent two states—on and off, yes or no, 1 or 0. When you launch an app, play a video, or save a document, the information passes through binary converters to transform human-readable input into machine language and back again.

For instance, when analyzing stock market data, financial software converts decimal numbers representing prices and volumes into binary to perform calculations quickly and accurately. This conversion lets computers process vast amounts of data in real time, enabling traders and analysts to receive timely insights without lag.

Remember, without efficient binary conversion, today's data-heavy tasks would crawl at a snail’s pace.

Machine instructions

Every command your device runs is broken down into machine instructions: sequences of binary code that tell the processor what to do. Binary converters play a key role by translating more understandable code (like assembly language) into this raw binary format. This is crucial because the processor hardware understands only binary.

Think of it like translating English instructions into a dialect that the machine speaks fluently. When a trader clicks "buy" on a trading app, behind the scenes, these instructions are swiftly converted into binary commands that execute the trade across electronic markets.

Role in Digital Electronics

Microcontrollers

Microcontrollers are tiny computers embedded in many devices, from coffee makers and cars to industrial machines. These rely heavily on binary converters to interpret inputs (like sensor readings) and execute programmed responses using binary-coded instructions.

For example, a smart thermostat uses a microcontroller to convert temperature readings into binary data it can process. Then it decides whether to turn the heating on or off. Without this binary translation, intelligent automation would be impossible.

Communication protocols

Communication protocols govern how digital devices exchange data. Binary converters ensure that information transmitted over networks or serial connections is correctly encoded and decoded in binary format. This consistency is vital for maintaining error-free communication.

Consider a financial broker receiving live market feeds. Those feeds come as binary data packets following a specific protocol. Converters translate these into comprehensible figures and graphs that help the broker make split-second decisions.

In short, the invisible work of binary converters keeps information flowing smoothly across countless devices and systems crucial to daily operations in computing, electronics, and communication.

By understanding these applications, investors, traders, and educators can appreciate the technical fundamentals driving modern technology and digital communications. Binary converters aren’t just abstract concepts; they’re key enablers of the device ecosystem we rely on every day.

Learning to Convert Manually

Mastering manual binary conversion is more than just an academic exercise; it builds a strong foundation for understanding how computers think and work. When you take the time to perform conversions by hand, you get a clearer picture of how data moves and transforms inside digital devices. This hands-on approach sharpens your grasp of number systems, making it easier to spot errors and understand algorithms used in programming and electronics.

Why Understanding Manual Conversion Matters

Enhances number system comprehension

Doing conversions manually helps demystify binary numbers. When you physically carry out the steps—like dividing a decimal number by 2 and noting down remainders—you start to see patterns that automated tools can hide. This approach clarifies how bits represent different powers of two, which is essential when decoding or encoding data. For instance, converting the decimal number 13 to binary manually (which is 1101) reveals exactly which bits are turned on and why. This knowledge is useful not only for digital tech enthusiasts but also for anyone who wants to strengthen their math skills in a very practical way.

Supports programming fundamentals

Understanding how binary conversion works by hand lays critical groundwork for programming. Programmers regularly work with data stored in binary form, so knowing how to switch between representation systems directly impacts debugging and writing efficient code. For example, bitwise operations in programming languages like C or Python rely on a solid grasp of binary values. When you’re familiar with manual conversions, it’s much easier to anticipate how algorithms manipulate those bits, ultimately making you a better developer or analyst.

Practicing Conversion Examples

Simple decimal to binary

Starting with straightforward exercises like converting 27 from decimal to binary is a great way to build confidence. Divide 27 by 2 repeatedly and jot down the remainders:

1. 27 ÷ 2 = 13, remainder 1

2. 13 ÷ 2 = 6, remainder 1

3. 6 ÷ 2 = 3, remainder 0

4. 3 ÷ 2 = 1, remainder 1

5. 1 ÷ 2 = 0, remainder 1

Reading the remainders backward gives you 11011, the binary form of 27. Doing this yourself makes the process stick and enables you to quickly convert numbers without a calculator.

Binary to decimal practice problems

On the flip side, converting binary numbers like 101101 back to decimal lets you see how each bit corresponds to a value. Multiply each bit by its power of 2 and sum them:

• (1 × 2^5) + (0 × 2^4) + (1 × 2^3) + (1 × 2^2) + (0 × 2^1) + (1 × 2^0)

• = 32 + 0 + 8 + 4 + 0 + 1 = 45

Such examples solidify your ability to interpret raw binary data, a useful skill when working with low-level programming or unpacking data protocols.

Practice is key. By working through manual conversions regularly, you'll naturally develop the ability to diagnose issues, write efficient code, and communicate technical insights clearly—skills highly prized in investment, trading, and tech fields alike.

Keeping manual conversion sharp not only deepens your comprehension but also boosts your confidence when dealing with binary data, whether you're handling financial models, analyzing digital signals, or teaching others the fundamentals.

Challenges with Binary Conversion

Binary conversion is a foundational skill in computing, but it doesn’t always go smoothly. Several challenges often trip up learners and professionals alike, especially those new to the concept. Understanding these pitfalls is crucial, as even minor errors can cause major issues in data handling or processing. In this section, we’ll explore the common hurdles faced during binary conversion, why they matter, and how to tackle them effectively.

Common Mistakes to Avoid

Incorrect Bit Placement

One of the prime sources of error when converting numbers to or from binary is the incorrect placement of bits. Because binary works on positional values where every bit has a specific weight (1, 2, 4, 8, and so forth), putting a digit in the wrong spot can completely alter the number’s value. For instance, accidentally shifting a bit to the left by just one position doubles the assumed value, leading to wildly inaccurate results.

For example, converting the decimal number 13 into binary should give you 1101. But if you mistakenly write it as 1011 or 1110, the binary value now represents a completely different decimal number (11 or 14). This mistake is easy to make if you aren’t vigilant or if you rush through the process. To minimize these errors, always count and label positions starting from the right (least significant bit) and move leftward carefully.

Misunderstanding Place Values

Closely tied to bit placement is misunderstanding place values in binary conversions. Many people are accustomed to decimal, where place values increase by powers of 10. Binary, on the other hand, uses powers of 2. Overlooking this key difference can lead to errors like treating binary digits as if they had decimal weight.

So, for a binary number like 1010, the place values from right to left are 1 (2^0), 2 (2^1), 4 (2^2), and 8 (2^3). Mistakenly interpreting these as decimal place values means you'd value those bits as 1, 10, 100, and 1000 instead—which nixes the whole point of binary. A good way to avoid this is to memorize the powers of two or keep a quick reference chart handy when practicing conversions.

Troubleshooting Conversion Errors

Step Verification

Checking your work regularly helps catch mistakes early. Step verification means going over each stage of your conversion thoroughly before moving on. Let’s say you’re converting decimal 25 to binary. After dividing and noting remainders, double-check each remainder in order, ensuring none are skipped or accidentally recorded twice.

If using manual methods, write out every division step and remainder clearly. When using tools, verify the digital output with a quick manual check for smaller numbers. This practice helps root out simple errors that cascade into bigger miscalculations.

Rechecking each conversion step isn’t just about correctness; it builds a stronger understanding of the process, making future conversions quicker and less error-prone.

Use of Double-Check Methods

Employing more than one technique to convert a number enhances accuracy. For example, after converting decimal to binary using division by 2, convert the binary result back to decimal to confirm it matches the original number. This ‘round-trip’ checking is a solid way to confirm your binary is spot-on.

Another approach involves using software tools or online converters alongside manual methods. By comparing results, discrepancies pop up immediately and can be corrected before they cause problems in contexts like coding or electronics.

In short, don’t rely on a single conversion pass—double-checking acts as a safety net to catch those sneaky errors that crop up even for seasoned pros.

Mastering these troubleshooting steps and avoiding those common mistakes ensures the integrity of your data throughout binary conversions. This reliability is what makes binary converters in computing and electronics so indispensable to investors, programmers, educators, and analysts alike.

Beyond Binary: Other Number Systems and Their Converters

While binary stands as the cornerstone of digital systems, it’s hardly the only number system that plays a role in computing and data representation. Expanding our view beyond binary to include octal and hexadecimal systems brings practical benefits, making complex data easier to read and manipulate. These alternative bases serve as shorthand notations or bridge systems, simplifying interactions with long binary sequences.

For instance, octal and hexadecimal reduce long strings of binary digits into manageable chunks, enabling programmers and analysts to quickly interpret data without getting lost in zeros and ones. Understanding these systems helps not just in programming but also in debugging, memory addressing, and even digital circuit design, where clear representation vastly improves clarity.

Octal and Hexadecimal Basics

Explanation of octal and hexadecimal

Octal (base-8) and hexadecimal (base-16) are number systems that condense binary’s complexity by grouping bits. Octal groups bits in threes because 2^3 equals 8, meaning every 3 binary digits translate directly into one octal digit. Hexadecimal works by grouping four binary digits, since 2^4 equals 16, mapping each quartet to one hex digit.

To illustrate, the binary number 11010110 becomes 326 in octal and D6 in hexadecimal. This shrinkage makes it easier to visualize and work with, especially when dealing with extensive binary strings.

Why they matter in computing

The use of octal and hex isn’t just for convenience. Many computing systems and programming environments adopt these systems due to their alignment with binary logic. Microprocessor instructions, memory dumps, and color codes in web design often utilize hexadecimal because it allows for quick pattern recognition and concise data notation.

Moreover, because hardware components like microcontrollers often group signals in chunks corresponding to these number bases, octal and hex serve as natural interfaces between hardware and human-readable code. This means fewer errors when dealing with low-level system operations, as humans can better parse information represented this way.

In short, octal and hexadecimal act as translators, helping programmers and engineers talk to machines without drowning in binary.

Converting Between Systems

Binary to octal and hexadecimal

Converting from binary to octal or hexadecimal is straightforward because of their bit-grouping nature. Start by splitting the binary number into groups:

• For octal: group bits in sets of three from right to left

• For hexadecimal: group bits in sets of four from right to left

Each group directly corresponds to a single octal or hex digit, which you can find by converting the group to decimal and then mapping to the proper digit or letter (for hex digits 10-15, represented as A-F).

For example, take the binary 10111100:

• Group it as 10 111 100 for octal, which converts to 2 7 4 → octal 274

• For hexadecimal, group as 1011 1100, which converts to B C → hex BC

This method is quick and less error-prone than converting through decimal as an intermediate step.

Decimal to octal and hexadecimal

Going from decimal to octal or hexadecimal usually involves repeatedly dividing the decimal number by 8 or 16, respectively, collecting remainders to build the new number:

1. Divide the decimal number by the base (8 or 16).

2. Note the remainder; this will be one digit in the new base.

3. Use the quotient for the next division.

4. Repeat steps until the quotient is zero.

5. The converted number is the remainders read in reverse.

For instance, converting 156 to hex:

• 156 ÷ 16 = 9 remainder 12

• 9 ÷ 16 = 0 remainder 9

Remainders reversed: 9 and 12 (which is C in hex), so decimal 156 is 9C in hex.

These systematic conversions are essential for anyone working closely with data at various abstraction layers, helping to cross-reference numerical values and troubleshoot errors efficiently.

Understanding these other number systems and how to convert between them equips traders, analysts, and educators alike to handle data formats encountered in coding, digital finance platforms, or technical documentation. It’s a crucial step beyond binary that demystifies the diverse formats defining modern computing.