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In this episode, we introduce two essential notational systems used throughout computing—binary and hexadecimal. You will learn what these number systems are, why they matter in information technology, and how to work with them using simple math and logic. Binary and hexadecimal are not just academic ideas. They appear in system diagnostics, memory analysis, network addressing, and more. This topic lays the foundation for future episodes on storage, addressing, and data manipulation, all of which build on the understanding of how values are represented and interpreted in digital environments.
Binary and hexadecimal are a core part of Domain One in the ITF Plus exam. They fall under the notational systems category and are often tested through vocabulary, basic math, and format recognition. While you won’t be asked to solve complex equations, you will need to identify binary and hex values, convert small numbers, and know where these systems appear in practice. Questions may involve classifying a format, choosing a conversion, or identifying where a number system is used in computing.
A number system is a way of representing values using digits and a base. Decimal is base ten and uses digits zero through nine. Binary is base two and uses only zero and one. Hexadecimal is base sixteen and uses digits zero through nine, followed by letters A through F. Each system defines how many unique symbols are available in a single place value. The base determines how numbers grow as digits are added. Learning to switch between these systems allows you to read values the way computers interpret them.
Binary is the simplest digital number system and is the language of computers. It is a base-two system using only the digits zero and one. Each binary digit is called a bit. Because hardware operates on two-state signals—such as high and low voltage, or on and off—it makes sense to represent data using just two values. Every operation in computing, from adding numbers to storing files, is ultimately built on strings of binary digits that represent logical states or encoded data.
Computers use binary because it aligns with their electrical design. Digital circuits are designed to detect the presence or absence of voltage. A one may indicate a high signal, and a zero may indicate a low signal. These two options are easy to detect, reliable to transmit, and inexpensive to manufacture. Because binary only uses two values, the system can process and store information with extreme precision and durability, making it ideal for computing environments at every scale.
Understanding binary place values is the first step in reading binary numbers. In decimal, each digit represents a power of ten. In binary, each digit represents a power of two. The rightmost digit is the ones place, then the twos place, then the fours, and so on. Each time you move left, the value doubles. For example, the binary number one zero zero represents the decimal number four. Recognizing this pattern makes binary math easier and helps you decode values by hand when needed.
To convert binary to decimal, add the place values that correspond to binary ones. For example, the binary number one one zero one contains a one in the eight’s place, a one in the four’s place, a zero in the two’s place, and a one in the one’s place. Add those values—eight plus four plus zero plus one—and the result is thirteen. This conversion method helps you quickly translate between what a computer sees and what a user understands.
The reverse conversion—from decimal to binary—uses division. Divide the decimal number by two repeatedly, recording the remainder each time. Once the number reaches zero, write the remainders in reverse order. For example, to convert thirteen to binary: thirteen divided by two is six remainder one, six divided by two is three remainder zero, three divided by two is one remainder one, and one divided by two is zero remainder one. Reading the remainders from bottom to top gives you one one zero one.
Hexadecimal is another number system used widely in computing. It is a base-sixteen system, which means each digit can represent values from zero to fifteen. Digits zero through nine represent themselves, and digits ten through fifteen are represented as the letters A through F. For example, A equals ten, B equals eleven, and F equals fifteen. Each hexadecimal digit corresponds to exactly four binary digits, making it a compact and readable way to express binary information.
One of the biggest advantages of hexadecimal is how compact it is. Because each hex digit maps to four binary digits, long binary strings can be written more cleanly. For example, the binary string zero zero one zero one one one one becomes the hexadecimal number two F. To convert hex to binary, replace each digit with its four-bit binary equivalent. To go from binary to hex, divide the binary number into four-bit groups and convert each to its hex equivalent.
Hexadecimal is used in many areas of information technology. It appears in MAC addresses, memory locations, IP version six addresses, and color codes in web design. It’s also common in system tools, BIOS screens, and diagnostic logs. Hexadecimal makes these outputs easier for humans to read, reducing errors and improving clarity. Because it simplifies long binary values, hex is favored when humans need to interpret raw data efficiently.
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Binary and hexadecimal play major roles in addressing and identification systems like I P addresses and MAC addresses. In I P version six, addresses are displayed using hexadecimal, making it easier to read and interpret compared to long binary strings. MAC addresses—used to identify network hardware—are commonly shown in hexadecimal format with pairs of characters like A C or 1 D. Behind the scenes, though, all of these identifiers are ultimately made up of binary digits. Binary is the native language of computing, and hexadecimal is the shorthand that humans use to read and write those binary values more easily.
Binary is also foundational in understanding file sizes and digital storage. Every bit is a single binary digit, and eight bits make up a byte. File sizes—such as kilobytes, megabytes, and gigabytes—are measured in powers of two, not ten, because they originate from binary values. For example, one kilobyte is one thousand twenty-four bytes, not one thousand. These units reflect how computers store and reference data, and understanding their binary basis helps make sense of why file sizes and memory behave the way they do.
Hexadecimal is widely used in memory management and low-level system operations. Memory addresses in RAM are often displayed in hexadecimal format because it compresses lengthy binary values into shorter, human-readable blocks. When you see memory ranges in system diagnostics, firmware settings, or error logs, they will usually be written in hexadecimal. This allows developers and technicians to quickly identify specific locations or data points, making troubleshooting and system inspection much more efficient.
Relating binary, decimal, and hexadecimal helps you understand that all number systems represent the same values in different formats. For example, the decimal number fifteen is written as one one one one in binary and as F in hexadecimal. The value is the same—it’s just represented differently. Being able to convert between these formats increases your flexibility and deepens your understanding of how data is stored, transmitted, and interpreted in a computing environment.
You can quickly improve your binary math skills by memorizing powers of two. These include one, two, four, eight, sixteen, thirty-two, sixty-four, and one hundred twenty-eight. When you know these values, you can convert binary to decimal by simply matching place values. Recognizing common binary patterns becomes easier, and your speed increases on questions that require quick mental math. This memorization helps especially during timed testing or troubleshooting scenarios.
On the ITF Plus exam, you may see several question types related to these number systems. Some questions may ask you to identify which number system is being used in a value. Others might require you to convert a small number from binary to decimal or from hex to binary. You might also be asked to recognize a practical application—such as identifying a MAC address or interpreting a hexadecimal error code. Practicing these scenarios can help reinforce both recognition and calculation.
There are many tools available to help with number system conversions. The built-in calculator in Windows has a Programmer mode, which lets you enter numbers in one format and instantly view the equivalents in binary, decimal, or hexadecimal. There are also dozens of free websites that offer converters. While these tools are useful, it’s still important to practice conversions manually, especially for small numbers, so that you fully understand the logic and can apply it during the exam.
Several misconceptions can make binary and hexadecimal seem harder than they really are. One common belief is that binary is difficult because it uses only two digits. In fact, once you learn to recognize place values, binary is much simpler than decimal. Another misconception is that hexadecimal is arbitrary or strange. In reality, hex is structured, predictable, and designed to match binary precisely. Finally, some learners assume that decimal is the only "real" number system, but in computing, binary and hex are just as real and far more useful.
Repetition is the key to mastering these number systems. Start by practicing simple conversions from binary to decimal and back. Make a reference chart showing binary values for the first sixteen numbers alongside their hex equivalents. Review this chart regularly to reinforce your memory. Use flashcards, mental math, or even game-based apps to build fluency. Repetition improves not only speed but confidence, making it easier to handle related topics later in the course.
Looking ahead, the next episode will cover decimal and octal number systems. These complete the picture of common notational systems found in IT and help round out your understanding of how data is structured. Decimal remains important for user-facing values, while octal appears in older systems and specific types of file permissions. Once you’ve explored all four, you’ll have the complete foundation needed to understand data measurement, binary storage, and memory addressing at the fundamental level.
To summarize, binary is the native language of computers—used at every level from storage to communication. Hexadecimal provides a more readable and compact way to express binary values, especially for users and technicians. Understanding both systems builds the foundation for working with memory, networking, file structures, and digital logic. These number systems are not only tested on the exam—they’re part of every system you’ll encounter throughout your IT career.