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In this episode, we complete our overview of notational systems by exploring the decimal and octal number systems. Decimal, or base ten, is the system most people are familiar with. It’s used in daily life, and it appears frequently in user-facing parts of computing. Octal, or base eight, is less common today but still appears in legacy systems, permissions models, and exam content. By understanding both, you’ll be better equipped to handle questions about conversions, data formats, and binary logic.
These number systems are part of Objective One point Two on the CompTIA ITF Plus exam. Decimal and octal both appear in different contexts—decimal often as output or measurement, and octal in system-level configurations or legacy formats. While the exam will not test you on advanced math, it will expect you to recognize these systems, perform small conversions, and understand how they relate to computing tasks. That’s why this episode is designed to support clarity and exam readiness.
The decimal system is the one you already know. It’s a base-ten number system that uses digits from zero to nine. Each position in a number represents a power of ten. For example, in the number one hundred thirty-seven, the digit one is in the hundreds place, the three is in the tens place, and the seven is in the ones place. These positions are based on ten raised to the zero, first, and second powers. This system forms the basis for all general-purpose arithmetic used in daily computing.
Understanding decimal place values is important for comparisons and conversions. The rightmost digit in a decimal number represents the ones place—ten raised to the zero power. As you move left, the digits represent tens, hundreds, thousands, and so on, each multiplying by an additional power of ten. So the decimal number one hundred thirty-seven is calculated as one times one hundred, plus three times ten, plus seven times one. These place values are important when converting to or from other number systems.
In information technology, decimal appears in many user-facing formats. System error codes are often displayed in decimal. Data measurements, such as percentages or processor usage, are typically shown in base ten for readability. Decimal is also the target for most conversions—when binary or hex values need to be explained to a user, they’re usually translated into decimal. Understanding decimal notation helps bridge the gap between how systems process data and how humans interpret it.
Octal is a base-eight system that uses digits zero through seven. Each digit represents a power of eight. This system is less common in everyday computing but still plays a role in system configurations and legacy data formats. Each octal digit expands differently than decimal or binary. Because the highest digit in octal is seven, place values increase more slowly than in decimal, making it useful in early computing when data had to be represented compactly but still be readable.
Octal place values are based on powers of eight. The rightmost digit is the ones place—eight raised to the zero power. The next digit is the eights place, then sixty-fours, and so on. For example, the octal number one two five is calculated as one times sixty-four, plus two times eight, plus five times one. That adds up to eighty-five in decimal. This conversion pattern is similar to decimal, but uses different base multipliers.
To convert from octal to decimal, multiply each digit by its corresponding place value and add the results. Start with the rightmost digit as the ones place, then move left to the eights, then sixty-fours, and so on. For example, octal one seven would be one times eight plus seven times one, which equals fifteen. Once you know the pattern, you can convert manually or use a calculator, depending on the situation. Recognizing the format quickly helps during timed exams.
Converting from decimal to octal uses division. Divide the decimal number by eight repeatedly, tracking the remainder each time. When the result reaches zero, write the remainders in reverse order to get the octal equivalent. For example, converting eighty-three to octal starts with eighty-three divided by eight, which gives ten remainder three, then ten divided by eight gives one remainder two, and one divided by eight gives zero remainder one. Writing those remainders in reverse gives one two three in octal.
Historically, octal served as a shorthand for binary in early computing. One octal digit equals exactly three binary digits, which made it convenient for programmers and hardware developers. In older UNIX systems, file permissions were commonly assigned using octal values. Instead of writing out long binary or hex numbers, octal provided a balance between readability and compactness. Each digit provided enough detail to express small binary blocks while staying easy to interpret.
You’ll still find octal in use today, especially in Linux and UNIX-based systems. File permissions are often represented using three-digit octal codes such as seven five five. This format tells the system how to manage read, write, and execute privileges for users, groups, and others. You might also find octal values in embedded systems or in documentation that references legacy formats. While less common in mainstream applications, octal remains an active topic in specific parts of IT.
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Binary and octal have a direct relationship based on place values. Because one octal digit corresponds to three binary digits, you can convert between the two by grouping binary bits in threes from right to left. For example, the binary number one zero one zero one one becomes groups of zero one zero, one zero one, and one one, which converts to two, five, and three in octal. This direct mapping made octal a useful shorthand in early systems when memory and display space were limited.
Octal has declined in popularity in modern computing, largely replaced by hexadecimal, which offers a more compact and scalable format. While octal expresses three binary digits per symbol, hexadecimal expresses four, allowing longer binary strings to be represented with fewer digits. This makes hexadecimal more readable and efficient for documentation, addressing, and debugging. Still, octal remains in use for specific applications, especially in file permissions and legacy systems.
Each number system serves a specific role in computing tasks. Decimal is used for user-facing measurements and numeric values. Octal often appears in low-level configuration or file system permissions. Hexadecimal is favored for memory addressing, color coding, and MAC addresses. Binary is the foundation of all digital logic. When you understand how each system fits into computing workflows, you can better interpret what data represents and why it appears in a specific format.
Examples often combine number systems in real-world applications. A file might display its size in decimal, but use octal values to define permission settings. Network tools show port numbers in decimal, while address fields may include hexadecimal characters. Being able to switch between these systems helps technicians interpret system outputs and perform conversions when troubleshooting or configuring equipment. Context will often reveal which system is being used.
The ITF Plus exam includes scenarios that require identification or conversion between number systems. You may be asked to classify a value as decimal, binary, or octal. Some questions present a conversion task, such as translating an octal value to decimal. Others may ask for comparison, requiring you to understand the range and base of each system. These questions test not only math ability but also familiarity with where each system appears in everyday computing.
There are several strategies for mastering octal more efficiently. Start by memorizing the digits zero through seven and their three-digit binary equivalents. Practice converting simple decimal values, such as twenty or forty, into octal using manual division. If you’re familiar with Linux or UNIX, use real-world permission values like seven five five or six four zero to reinforce your learning. These examples connect abstract number systems to practical use.
New learners often confuse the meaning of a base. The base of a number system indicates how many unique digits it uses. Decimal has a base of ten and uses digits zero through nine. Octal has a base of eight and uses digits zero through seven. The base does not refer to a starting point or a fixed value—it simply tells you how counting progresses. Prefixes or labeling often help clarify the system in use. For example, a value might be labeled “0o” for octal or “0x” for hex.
Multiple tools are available to help learners practice decimal and octal conversions. Programmer modes on calculators allow you to view numbers in multiple systems side by side. Online converters let you test your knowledge instantly. However, manual practice is still encouraged, especially for small numbers. Writing out conversions by hand strengthens your ability to perform them during an exam and helps you visualize how each digit contributes to the total.
Reviewing all four major number systems together provides a complete picture of how digital information is represented. Binary is base two, octal is base eight, decimal is base ten, and hexadecimal is base sixteen. Each serves a purpose in hardware logic, software design, or networking standards. The ITF Plus exam may test your understanding of more than one system in a single question. Being able to move fluently between them is a core part of technical fluency.
To summarize, decimal is the default system used by humans and appears in most user-facing displays. Octal is less common today but still plays a role in permissions and low-level configuration. Both systems tie directly back to binary logic, forming a foundational layer of computing design. Understanding how these systems relate to each other—and knowing how to convert between them—helps prepare you for the ITF Plus exam and builds your fluency in interpreting values across different environments.