Number Base Converter
Use only digits valid for the chosen base (binary 0–1, hex 0–9 / A–F).
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How to use
- 1 Type a number in any base field — binary (0/1), octal (0–7), decimal (0–9), or hex (0–9, A–F).
- 2 All other base fields update in real time as you type.
- 3 Hex values follow the standard prefix-free format (FF instead of 0xFF). Color codes work both ways — type FF5733 to see the swatch, or type a decimal to convert and preview.
- 4 Use this for bit-mask debugging, hex color codes, file permissions (octal 755), Unicode code points (U+1F600), and assembly-language values.
- 5 For two's complement signed values, manually convert: 0xFFFFFFFF interpreted signed = −1; interpreted unsigned = 4,294,967,295.
About Number Base Converter
FAQ
Q How do I convert binary to decimal manually?
Multiply each bit by 2 raised to its position from the right (starting at 0) and sum. For 1011₂: 1×8 + 0×4 + 1×2 + 1×1 = 11₁₀. For longer values, group into nibbles (4 bits) and use the hex shortcut: 1011 = B, 1101 0011 = D3 = 211 in decimal.
Q What is hex FF in decimal?
Hex FF equals 255 in decimal — the maximum value of a single byte (8 bits). It's 1111 1111 in binary. RGB color hex pairs run from 00 (0) to FF (255), giving 256 intensity levels per channel. The full white #FFFFFF is the maximum value for all three channels.
Q Why does chmod 755 mean rwxr-xr-x?
Each digit is the sum of read (4), write (2), and execute (1) for one user class. The first 7 = 4+2+1 = read+write+execute (rwx) for the owner. The middle 5 = 4+0+1 = read+execute (r-x) for group. The last 5 = read+execute (r-x) for everyone else. So 755 means: owner can do anything, others can read and run.
Q How do I read a memory address like 0x7FFE5234?
It's hexadecimal — each digit represents 4 bits. 0x7FFE5234 = 7 × 16⁷ + F × 16⁶ + ... = 2,147,001,396 in decimal. The 0x prefix is C-language convention for hex; CSS uses # (#FF5733); some assemblers use $ or h suffix.
Q What is two's complement and why is 0xFFFFFFFF = −1?
Two's complement is how computers represent signed integers. The leftmost bit is the sign: 0 = positive, 1 = negative. To negate, flip all bits and add 1. So 0x00000001 (=1) negated becomes 0xFFFFFFFE + 1 = 0xFFFFFFFF, which interpreted as signed int = −1, but as unsigned = 4,294,967,295. The same bits, two meanings.
Q Why is 1024 KB called 1 MB sometimes but 1000 KB other times?
Two competing standards. Binary (IEC) uses powers of 2: 1 KiB = 1024 B, 1 MiB = 1024 KiB. Decimal (SI) uses powers of 10: 1 KB = 1000 B, 1 MB = 1000 KB. Storage manufacturers use SI (a 1 TB drive = 10¹² bytes); operating systems often use IEC. The 1 TB drive shows 931 GB in Windows because Windows uses GiB (1024³).
Q How do I convert hex color FF5733 to RGB?
Split into three pairs: FF=255 (red), 57=87 (green), 33=51 (blue). So #FF5733 = rgb(255, 87, 51) — a vivid orange-red. Type FF5733 in this calculator's hex field to see the swatch and the decimal split. CSS accepts both formats interchangeably.
Q What's the difference between octal 0o755 and decimal 755?
Octal 0o755 (or just 755 in chmod context) is base 8, equivalent to 7×64 + 5×8 + 5 = 493 in decimal. Decimal 755 is just seven hundred fifty-five. The shared digit pattern is coincidental. Modern Python and JavaScript require the 0o prefix to disambiguate; older C used a leading 0 (which still works but is error-prone).
Official resources
IEEE Std 754 — Floating-Point Arithmetic
Authoritative IEEE standard defining binary floating-point representation used in all modern CPUs.
NIST — SI prefix definitions
NIST official explanation of binary (KiB, MiB) versus decimal (KB, MB) prefixes for digital storage.
IETF RFC 4648 — Base16/32/64 Encoding
IETF specification for Base16 (hex), Base32, and Base64 data encodings.
W3C CSS Color Module Level 4
W3C standard defining CSS color hex notation and other color formats.