Binary, Decimal, and Hexadecimal: Number Systems Explained for CompTIA Tech+ (ITF+)

Why Number Systems Matter in IT

Every computer you have ever touched does its thinking in a number system that has nothing to do with the ten digits you grew up counting on. The CompTIA Tech+ (FC0-U71, formerly ITF+) exam tests this directly, because number systems are not trivia — they are the foundation underneath IP addressing, memory addresses, color codes, file permissions, and the MAC address burned into every network card. If you can convert comfortably between decimal, binary, and hexadecimal, a whole category of IT concepts stops feeling like memorization and starts feeling like arithmetic.

The Decimal System: What You Already Know

Decimal is a base-10 system, meaning it uses ten symbols (0 through 9) and each position in a number represents a power of 10. The number present in daily life, 347, really means (3 × 10²) + (4 × 10¹) + (7 × 10⁰). That positional-value idea — where a digit's worth depends on where it sits — is the one concept that carries over to every other number system, including the two a computer actually prefers.

The Binary System: The Language of Computers

Binary is base-2. It uses only two symbols, 0 and 1, because those map directly onto the two states a transistor or a magnetic storage cell can hold: off/on, no-charge/charge, low-voltage/high-voltage. Every position in a binary number represents a power of 2 instead of a power of 10, so the rightmost bit is worth 1, the next is worth 2, then 4, 8, 16, 32, 64, and 128 for a standard 8-bit byte.

A single binary digit is called a bit. Eight bits grouped together form a byte, and a byte can represent 256 distinct values (2⁸), numbered 0 through 255. That 0–255 range should look familiar to anyone who has worked with IPv4 addressing, and that is not a coincidence — it is the exact reason each octet in an IPv4 address tops out at 255.

Converting Between Decimal and Binary

To convert decimal to binary, repeatedly divide by 2 and record the remainders from bottom to top, or use the positional-value table (128, 64, 32, 16, 8, 4, 2, 1) and subtract the largest value that fits at each step. For example, 203 breaks down as 128 + 64 + 8 + 2 + 1, giving the binary value 11001011.

To go the other direction, add up the place values wherever there is a 1. The binary value 10110100 is 128 + 32 + 16 + 4 = 180 in decimal. Tech+ candidates are not expected to do this instantly in their heads, but they are expected to recognize the pattern and work through a byte-sized conversion without a calculator.

The Hexadecimal System: A Compact Shorthand for Binary

Hexadecimal is base-16. It needs sixteen symbols, so after 0 through 9 it continues with the letters A through F, where A = 10, B = 11, C = 12, D = 13, E = 14, and F = 15. Hex exists for a very practical reason: one hexadecimal digit represents exactly four binary digits (a "nibble"), so a full byte can be written as just two hex characters instead of eight error-prone 1s and 0s. The byte 11111111 in binary is simply FF in hex — far easier for a human to read, type, and remember correctly.

Converting Between Hexadecimal, Binary, and Decimal

Because each hex digit maps to exactly four bits, converting hex to binary is a lookup, not math: split the hex number into digits, and replace each with its 4-bit binary equivalent. The hex value 2F becomes 0010 1111, since 2 = 0010 and F = 1111. To convert hex to decimal, multiply each digit by the matching power of 16: 2F = (2 × 16) + (15 × 1) = 47.

This 4-bits-per-digit relationship is why hexadecimal shows up wherever binary data needs to be displayed compactly: MAC addresses, color codes in web design (#FF5733), memory addresses, and hash values like MD5 or SHA checksums are all hexadecimal under the hood.

Where You'll See These Number Systems in Real IT Work

Number systems stop being abstract the moment you look at where they actually appear on the job:

• IPv4 addressing — every address is really four binary octets displayed in decimal for human convenience. Understanding that relationship is what makes IPv4 address classes and ranges like the ones defined in RFC 1918 make sense instead of needing to be memorized as arbitrary numbers.
• Subnetting — borrowing bits from the host portion of an address to create subnets is pure binary manipulation. Once binary clicks, techniques like VLSM (Variable Length Subnet Masking) go from confusing to mechanical.
• MAC addresses — the physical address burned into a network interface is a 48-bit value displayed as twelve hexadecimal characters (for example, 00:1A:2B:3C:4D:5E). That hex formatting is exactly why attacks like MAC flooding reference tables full of hex values rather than decimal ones.
• Port numbers — while ports themselves are expressed in decimal, they are stored as 16-bit binary values, which is exactly why the usable range tops out at 65,535 (2¹⁶ − 1). Knowing which numbers matter most is covered in Port Numbers to Know for the A+, Network+, and Security+ Exams.
• Color codes and file permissions — web hex color codes (#1A73E8) and Linux octal permissions (which you will meet again at base-8) both reuse the same positional-value logic as binary and hex.

CompTIA Tech+ (ITF+) Exam Tips

Tech+ (exam FC0-U71) covers number systems under its "Compare and contrast notational systems" objective, and the exam favors recognition and simple conversion over speed math. A few tips that consistently help candidates:

• Memorize the powers of 2 up to 256 (1, 2, 4, 8, 16, 32, 64, 128, 256) cold — nearly every binary conversion question builds on this list.
• Memorize hex-to-decimal for A through F (10–15) the same way you memorized your multiplication tables; this alone unlocks most hex questions.
• Practice converting a full byte in both directions until it takes under 30 seconds — the exam rewards familiarity, not formulas.
• Expect the exam to test why these systems exist (how computers represent data) at least as much as it tests raw conversion, so be ready to explain the concept in plain language, not just compute an answer.
• If you plan to continue toward Network+ or Security+ after Tech+, treat this topic as an investment: binary math underpins subnetting on Network+, and hex underpins hashing, MAC filtering, and memory forensics on Security+ and CySA+.

Key Takeaways

• Decimal (base-10), binary (base-2), and hexadecimal (base-16) are three ways of representing the same values; computers use binary natively because it maps to two physical states, and humans use hex as a compact, readable stand-in for binary.
• One hex digit always equals exactly four binary digits, which is why hex is used to display MAC addresses, color codes, and hash values.
• Comfort converting a single byte between all three systems is the single most useful skill this topic offers, both for the Tech+ exam and for every networking and security topic built on top of it.