Number Base Converter
Articles, guides, and in-depth tips for the Number Base Converter — everything you need to get the most out of it.
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Why Hex Won: One Digit, Exactly Four Bits
Why Your RTC Chip Returns 89 When the Time Is 59 — BCD, Gray Code, and Other Number Encodings in Modern Hardware
Binary-Coded Decimal (BCD) encodes each decimal digit as a 4-bit group — which is why real-time clock chips return 0x59 to mean 59 seconds (not 89), and why hardware with BCD limits constrains values to 0-99 rather than 0-255. Here's BCD in RTC hardware and financial calculations, Gray code's one-bit-change property that prevents rotary encoder errors, and why TCP checksums use one's complement arithmetic.
How to Read Hex Like a Debugger — Magic Bytes, Memory Dumps, and Why Byte Order Matters
Hexadecimal is a window into how computers represent data at the byte level — and once you can read it naturally, you start seeing structure in things that previously looked like noise. Here's how magic bytes identify file formats (JPEG starts with FF D8 FF, PDF with %PDF-, ZIP with PK), what hex reveals in network captures and memory dumps, the endianness problem that causes little-endian hex to read backwards, and the famous debug sentinel values like 0xDEADBEEF and 0xCAFEBABE.
IEEE 754 Floating-Point: Why 0.1 + 0.2 ≠ 0.3 and What to Use for Financial Calculations
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.
#FF5733, 00:1A:2B:3C:4D:5E, and IPv6: Three Everyday Hex Formats, Three Different Reasons for Hex
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 and Bitmasks: From Unix Permissions to Feature Flags
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.
Negative Numbers, Overflow, and What Hex Reveals About Your Data
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.
Number Base Converter — Binary, Octal, Decimal & Hex Explained
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.
