Number Systems, Bit by Bit
Binary, hexadecimal, and decimal aren't just abstract math - they're how every IPv4 address, subnet mask, and MAC address is actually stored and read by machines. Work through the three modules below to build fluency converting between them.
Understanding Binary, Decimal, and Hexadecimal
Computers represent and process data using different number systems. The three most common systems are Binary, Decimal, and Hexadecimal.
The decimal system is the number system we use in everyday life. It is a base-10 system, which means it uses 10 digits: 0 to 9.
The binary system is used internally by computers and digital devices. It is a base-2 system, meaning it uses only two digits: 0 and 1. Each binary digit is called a bit. Combinations of bits are used to represent numbers, characters, images, and instructions in a computer.
The hexadecimal system is a base-16 system used in computing because it provides a compact way to represent binary values. It uses 16 symbols: 0–9 and A–F, where: A = 10, B = 11, C = 12, D = 13, E = 14, and F = 15.
Understanding how to convert between these number systems is important in areas such as computer architecture, networking, cybersecurity, and digital electronics.
Binary → Decimal
Each bit represents a power of 2. Sum the place values where the bit is 1.
Hexadecimal → Decimal
Base-16 packs a full byte into just two symbols - you'll see this constantly in MAC addresses and memory dumps.
Decimal → Binary (8-bit · IPv4 Octets)
Every IPv4 address, like 192.168.1.1, is four octets - each one an 8-bit binary number from 0–255 (28 = 256 values). Check which place values 128, 64, 32, 16, 8, 4, 2, 1 fit.
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