Convertor de baze numerice

Convert between any number base, exactly

This number base converter shows binary, octal, decimal and hexadecimal side by side, plus an any-base field for every radix from 2 to 36. Edit any one value and the rest update live, so converting decimal to binary, hex to decimal, binary to hex or any other combination takes a single keystroke — no buttons to press and no page reloads.

It's a full number base converter calculator that handles the awkward cases too: negative numbers, a leading 0x, 0b or 0o prefix when you paste from code, and optional digit grouping to make long values readable.

Binary, octal, decimal and hexadecimal explained

A number's base (or radix) is simply how many digits it uses. Binary (base 2) is the language of hardware; octal (base 8) packs three bits per digit; decimal (base 10) is everyday counting; and hexadecimal (base 16) packs four bits per digit using 0–9 and A–F. The same quantity wears all four: decimal 250 is 11111010 in binary, 372 in octal and FA in hex.

See every conversion worked out, step by step

Turn on Show steps and the tool becomes a teaching aid. It expands a number to decimal with the positional method — each digit multiplied by its place value, e.g. binary 1101 = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 13 — and converts decimal to another base with the division-remainder method, listing every division and remainder so you can read the answer from the bottom up.

Choose any 'from' and 'to' base in the steps panel to follow conversions like binary to hex or base 10 to base 36. It's the rare number base converter with steps that shows the real arithmetic rather than just the result — useful for students checking homework or anyone learning how base conversion actually works.

Built for big numbers

Most converters quietly lose precision once a value passes the 64-bit mark, because they fall back to floating-point maths. rapidtables.com and calculator.net both have this limitation for very large inputs. This big number base converter uses JavaScript's arbitrary-precision BigInt, so a 300-digit decimal, a thousand-bit binary string or a long hexadecimal hash all convert exactly — every digit intact.

A live metrics row reports the bit length, byte count and the smallest standard width (8-, 16-, 32-, 64- or 128-bit) that holds your number, which is handy when you're sizing fields or checking whether a value overflows a specific data type.

How it compares to RapidTables and WolframAlpha

rapidtables.com is the go-to for quick conversions, but it uses separate pages per conversion direction (decimal to binary on one page, binary to decimal on another), tops out at base 16, and doesn't show step-by-step working. WolframAlpha shows steps but requires a Pro subscription for full working, sends every query to Wolfram's servers, and is slow for interactive use.

This converter puts all four bases on one screen, supports bases 2–36, shows full step-by-step working for free, handles arbitrarily large integers without precision loss, and runs entirely in your browser. No account, no subscription, no data sent anywhere. Works on iPhone, Android, tablet and desktop.

Private, instant and free

There's nothing to install and no account to create. Every conversion — from a single bit to a 1,000-digit integer — happens locally in your browser, so the numbers you convert never leave your device. Bookmark this number base converter and reach for it whenever you need to switch between binary, octal, decimal, hex or any base in between.

How place value works in any base

Every positional numeral system is built on one idea: a digit's contribution to the total equals digit × base^position, where positions are counted from zero starting on the right. In decimal (base 10) the number 347 means 3×10² + 4×10¹ + 7×10⁰ = 300 + 40 + 7. Swap the base to 2 and the same rule gives you binary; swap it to 16 and you get hexadecimal. The arithmetic is identical — only the base changes.

Humans settled on base 10 for an anatomical reason: ten fingers. Merchants and mathematicians who counted on their hands naturally fell into groups of ten, and the habit solidified across civilisations independently. Binary (base 2) exists for an entirely physical reason: transistors, the building blocks of every processor, have only two stable electrical states — on and off. Mapping those states to 1 and 0 makes binary the native language of hardware. No other base maps as cleanly onto the physics of a switch.

Understanding place value is the key to converting any number by hand. To read 10110 in binary: 1×2⁴ + 0×2³ + 1×2² + 1×2¹ + 0×2⁰ = 16 + 0 + 4 + 2 + 0 = 22 in decimal. Enable the Steps panel in this tool to watch that expansion play out digit by digit for any number you enter, in any source base.

Hexadecimal in everyday computing

The reason programmers gravitate to hexadecimal is a clean power-of-two relationship: one hex digit represents exactly 4 bits (called a nibble), so one 8-bit byte collapses to just two hex digits. The byte 11111111 in binary is FF in hex — far easier to read and type. A 32-bit value that would take 32 binary digits fits in 8 hex digits, and a 128-bit UUID fits in 32. Hex is binary made human-readable.

You encounter hexadecimal constantly without always noticing. CSS color codes like #FF5733 are three hex bytes: FF for red, 57 for green, 33 for blue. Memory addresses in debuggers and crash logs print as hex (0x7FFE4B2C). SHA-256 hashes are 64 hex digits (256 bits ÷ 4). MAC addresses such as A4:C3:F0:85:AC:2D are six hex bytes separated by colons. IPv6 addresses are eight groups of four hex digits, covering 128 bits in a compact form that would be unreadable in decimal.

The A–F letter digits in hexadecimal represent the values 10 through 15. That's not arbitrary — it's the minimum alphabet needed to express every possible nibble with a single character, keeping one-to-one parity between hex digits and 4-bit groups. Enter any CSS hex color or memory address into the Hexadecimal field of this converter and you'll immediately see its decimal value, its octal form, and its full 24- or 32-bit binary representation.

Octal and Unix file permissions

Octal (base 8) was an early favourite in computing because one octal digit maps exactly to three binary bits. On machines like the PDP-8 minicomputer of the 1960s, whose word size was a multiple of three bits, octal made debugging printouts far more compact than binary without any translation cost. Today octal is niche, but it survives in one very visible place: Unix and Linux file permissions.

The command chmod 755 sets a file's permissions to rwxr-xr-x. Each octal digit maps to three bits representing read (4), write (2) and execute (1) for owner, group and others respectively. The digit 7 = 4+2+1 = 111 in binary = read, write and execute. The digit 5 = 4+0+1 = 101 = read and execute only. The digit 5 repeated for the final group gives the same permissions to everyone else. A permission mask like chmod 644 (owner read/write, others read-only) becomes immediately obvious when you see 6 = 110 and 4 = 100 as binary triplets.

Octal is less common than hex today primarily because modern hardware is byte-oriented — bytes are 8 bits, not 6 or 9 — so octal digits don't align neatly with bytes the way hex digits do. Nevertheless, any Unix developer who works with chmod, umask or file-mode constants in C (S_IRWXU = 0755) is doing octal arithmetic. The Octal field in this converter lets you verify a permission mask at a glance: type 755 and instantly see the binary breakdown 111 101 101.

Binary arithmetic: two's complement, overflow, and bitwise operations

Computers store negative integers using two's complement, not a simple sign bit, because two's complement lets addition hardware work identically for positive and negative numbers. To negate a number in two's complement: flip every bit, then add 1. In an 8-bit register, −1 is represented as 11111111 — flip the bits of 1 (00000001) to get 11111110, add 1, and arrive at 11111111. Adding that to 00000001 gives 100000000, which overflows the 8-bit boundary and leaves 00000000 — exactly 0, which is the correct result of −1 + 1.

Overflow occurs when a result exceeds the register's bit width. In a signed 8-bit integer the maximum is 127 (01111111); adding 1 wraps it to 10000000, which two's complement interprets as −128. This is a real source of bugs in low-level code, which is why languages expose overflow-safe arithmetic and why knowing binary representation matters in practice.

Bitwise operations — AND, OR, XOR, NOT, and bit shifts — work on individual bits in parallel and appear everywhere in systems programming. AND with a mask zeroes out bits you want to ignore (flag testing: flags & 0b0100 isolates bit 2). OR sets bits (flags | 0b0100 switches bit 2 on). XOR toggles bits and is the basis of many fast checksum and encryption routines. A left shift by n multiplies by 2ⁿ; a right shift by n divides by 2ⁿ — both are cheaper than multiplication on most CPUs. Inspecting a number's binary form in this converter is the fastest way to reason about which bits a mask will affect.