Number Systems: Binary, Decimal & Hex

A number system is just a set of rules for writing numbers using a fixed set of symbols. The one you grew up with is decimal (base 10): ten digits, 0 through 9. Computers, though, store everything as electrical states that are either on or off, so at the hardware level they count in binary (base 2): only 0 and 1. Because long strings of 1s and 0s are painful for humans to read, we compress them into hexadecimal (base 16), where a single symbol stands for four binary digits. The value never changes across bases, only the way it is written down. The number forty-two is 42 in decimal, 0b101010 in binary, and 0x2A in hex, all the same quantity.

This is foundational for cybersecurity because the raw material of the field is bytes. You read hex dumps when analyzing a file or malware sample, you reason in bits when subnetting a network or writing a firewall rule, you see hex in MAC addresses, memory addresses, and cryptographic keys, and you decode encodings (ASCII, Base64, URL-encoding) that all rest on these three bases. If you cannot fluently move between binary, decimal, and hex, tools like xxd, tcpdump, and a subnet calculator stay opaque. Learn the conversions once and every one of those tools starts speaking a language you understand.

Each base has a radix (how many distinct digits it uses) and often a prefix that labels which base a written number is in. Decimal is the default and usually carries no prefix. Binary literals are commonly prefixed with 0b, and hexadecimal with 0x. The prefix matters: without it, 10 could mean ten, two, or sixteen depending on the base.

Memorizing this table is the single highest-value thing you can do. Sixteen values is exactly what one hexadecimal digit and one 4-bit nibble (half a byte) can each hold, so this chart is the bridge between binary and hex.

A bit is a single 0 or 1. A byte is 8 bits grouped together. In any base, each position is worth the radix raised to a power, and you find a number's value by multiplying each digit by its position value and adding them up. In binary the position values are the powers of two. Learn these eight and you can convert any byte in your head.

Binary to decimal — line the place values up under the bits and add the ones sitting over a 1: 1 1 0 0 1 0 1 0 128 + 64 + 0 + 0 + 8 + 0 + 2 + 0 = 202 Decimal to binary — subtract the largest power of two that fits, then repeat with what is left. For 45: 32 fits (13 left), 8 fits (5 left), 4 fits (1 left), 1 fits (0 left). Put a 1 in those positions and 0 everywhere else, giving 00101101. Hex to decimal — multiply each hex digit by 16 raised to its position. 0xCA = (C x 16) + A = (12 x 16) + 10 = 192 + 10 = 202. Binary and hex — use the nibble trick from the chart. 1100 1010 splits into C and A, so 11001010 = 0xCA. All three of these examples describe the same byte: 11001010 = 0xCA = 202.

Hex is everywhere in security tooling because two hex digits describe exactly one byte, which keeps binary data compact and readable. A CSS/HTML color like #FF5733 is three bytes: red = 0xFF = 255, green = 0x57 = 87, blue = 0x33 = 51. A MAC address is 48 bits written as six hex octets, such as 00:1A:2B:3C:4D:5E, where the first three octets identify the hardware vendor (the OUI). And every byte in a captured packet or a file shows up as a pair of hex digits when you dump it.

An IPv4 address is a 32-bit number, split into four 8-bit octets (four bytes) written in decimal and separated by dots. Because each octet is one byte, each part legally ranges from 0 to 255, which is why 256.0.0.1 is invalid. Under the hood the dotted-decimal form is just binary in disguise. Take 192.168.1.1: 192 = 11000000 168 = 10101000 1 = 00000001 1 = 00000001 So the full address in binary is 11000000.10101000.00000001.00000001. Reading it as bits is what lets you see where the network part ends and the host part begins, which is the whole idea behind subnet masks.

Work each conversion by hand first (place values / nibble trick), then check yourself with printf or python: 1. Find the row for cam-07. Convert its binary_id to decimal, then to hex by splitting it into two nibbles. Check with python -c "print(int('<binary_id>', 2))" and printf '%x\n' <the decimal answer>. 2. Find the row for switch-01. Convert its ip_last_octet to binary and to hex. Check with python -c "print(bin(<n>))" and printf '%x\n' <n>. 3. Find the row for badge-reader-3. Its badge_color_hex is a 3-byte RGB color: two hex digits each for red, green, and blue. Convert just the red byte to decimal (check with printf '%d\n' 0x<red byte>), then state the smallest and largest decimal value any single byte in that column could ever hold, and explain why.