A memory address shows up as 0x7ffee23a1c40. A file permission is 0755. A bitmask in a driver's documentation is written in binary. A color channel value needs converting from decimal to two-digit hex. None of these are difficult conversions individually, but doing them repeatedly in your head — especially binary to hex, which requires grouping bits into nibbles — is slower and more error-prone than it should be for something so mechanical.
Low-level programming, embedded development, networking, and even everyday web development (hex colors, again) all require moving between number bases regularly enough that keeping a mental lookup table for hex digits only gets you so far once numbers get larger than a byte or two.
Where This Trips People Up
Octal is the sneaky one. A file permission like 644 looks like a decimal number but is actually base 8, and treating it as decimal when reasoning about it leads to confusion about what the actual bit pattern is. Binary gets unwieldy past 16 bits — a 32-bit value in binary is thirty-two characters long, hard to read and easy to miscount when you are trying to isolate specific bits for a flag check.
Convert Between All Four Bases at Once
Bellows includes a number base converter that shows a value in decimal, hexadecimal, octal, and binary simultaneously. Type a number in any base and see all four representations update together — no separate conversion for each pair.
Low-Level and Embedded Work
Reading register values, bitmasks, and memory addresses in embedded firmware or systems programming means moving fluidly between hex and binary. Seeing both at once, alongside decimal, removes a layer of manual translation from an already detail-heavy task.
File Permissions and Networking
Unix file permissions, subnet masks, and various binary flags in networking protocols are commonly expressed in octal or binary but reasoned about in decimal. A quick conversion confirms exactly what a permission string or flag byte represents before you change it.