0.1 + 0.2 ≠ 0.3 in nearly every programming language — because 0.1 can't be represented exactly in binary. Here's the IEEE 754 bit structure (sign, exponent, mantissa), special values (NaN, Infinity, -0), why integers above 2^53 lose precision in JavaScript, and why financial code should never use floats.
Color codes, MAC addresses, and IPv6 addresses all use hexadecimal — but for different reasons rooted in what each format actually represents. Here's how hex's "two digits per byte" property makes color codes' three-channel structure visible at a glance, why MAC addresses' hex grouping aligns with manufacturer-ID lookups, why IPv6's 128-bit addresses would be unwieldy in decimal, and how the "::" shorthand compresses runs of zero-groups.
Bit manipulation is where number bases become practical: Unix permissions, feature flags, IP subnetting, and protocol fields all use bitmasks. Here's how AND, OR, XOR, and shifts work, with real examples from file permissions and flag systems.
Most developers can convert hex to decimal — but two's complement, signed overflow, and bit-width boundaries are where base conversion becomes genuinely useful for debugging real problems.
Learn how binary, octal, decimal, and hexadecimal number systems work, when each is used in programming, and how to convert between them instantly with a free number base converter.
