Choose the source radix first
Convert binary, decimal, hex, and octal integers
Enter a whole number within the bounded limit shown in the interface. Review every base at once, then choose padding, prefix, case, width, and signed interpretation deliberately.
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Enable JavaScript to convert and copy values. The base, width, signedness, and exactness guidance below remains readable.
Position determines value
How integer base conversion works
A positional numeral assigns each digit a value based on its place and radix. In binary, each position is a power of 2; in octal, a power of 8; in decimal, a power of 10; and in hexadecimal, a power of 16. Binary 101101 therefore represents 1×2⁵ + 0×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 45.
The converter parses the selected source notation as an integer and renders that same value in the other bases. It does not pass the value through an IEEE 754 floating-point approximation. This distinction matters for long identifiers, bit masks, checksums treated as numbers, database keys, and values above the range in which a JavaScript Number represents every consecutive integer.
Hexadecimal is a compact view of binary because one hex digit maps to exactly four bits. Octal maps one digit to three bits. Grouping the binary result into nibbles makes 11111111 visibly correspond to FF; grouping into triplets makes it correspond to octal 377.
This page is an integer converter, not a text decoder. Binary 01000001 can be the number 65 or an encoded byte for the letter A under ASCII and UTF-8. Use the Binary Translator only when bytes must be interpreted as text.
- Base 2
- Digits 0 and 1; one binary digit is one bit.
- Base 8
- Digits 0 through 7; one octal digit covers three bits.
- Base 10
- Digits 0 through 9; ordinary decimal integer notation.
- Base 16
- Digits 0 through 9 and A through F; one digit covers four bits.
- Scope
- Exact whole numbers within the bounded interface limit; no fractions.
A bit pattern needs a width
Mathematical negatives versus two's complement
The notation -5 is a mathematical negative integer. Its magnitude is five and the minus sign is separate from the binary digits. Two's complement instead interprets a fixed-width bit pattern as signed: the 8-bit pattern 11111011 represents −5, while the same eight bits represent unsigned 251.
Width is part of that meaning. The 8-bit pattern for −1 is 11111111; the 16-bit pattern is 1111111111111111. Removing leading ones before signed interpretation changes the field and can change the result. Select the width required by the register, protocol, file format, database type, or language API before using a signed view.
The signed range for width n is −2n−1 through 2n−1−1. The unsigned range is 0 through 2n−1. Values outside the selected range should produce an explicit diagnostic, not silent wrapping, unless the interface clearly labels a deliberate modulo operation.
11111111 is unsigned 255 or signed −1 at 8 bits. The digits alone do not choose between them.
Representation carries context
Prefixes, leading zeroes, grouping, and case
0b1010 · 0o12 · 0xAA language-style prefix records the intended radix but is not part of the mathematical value.00001010Padding preserves an 8-bit field even though the unsigned value is still decimal 10.1101 1110 1010 1101Nibble groups make the corresponding hexadecimal digits DEAD easier to verify.dead · DEADLetter case changes presentation, not value; follow the consuming format's convention.Keep assumptions visible
A reliable number-base conversion workflow
- 1
Select the source base
Do not infer whether bare
10means binary two, decimal ten, or hexadecimal sixteen from appearance alone. - 2
Choose sign and width
Use mathematical sign for ordinary integers. Choose a fixed width only when interpreting or emitting a two's-complement field.
- 3
Preserve required formatting
Apply padding, prefixes, grouping, and hex case after the value is understood, then copy the representation the consumer expects.
Local conversion with bounded work
Convert identifiers and bit fields without an API request
The current input is processed in this browser tab. LiveParse does not send the number to a conversion endpoint, store a conversion history, or look up its meaning in an external service. The interface displays a bounded input limit so parsing and rendering very long representations cannot monopolize the page.
Local conversion does not remove every privacy risk. Clipboard managers, browser extensions, screenshots, crash reporting, and other software on the device remain outside this page's boundary. Remove secrets before sharing a converted key, token field, memory address, or production identifier.
The implementation follows ECMAScript's arbitrary-precision integer model for exact whole-number work while applying explicit application limits. Review the ECMAScript BigInt definition and its fixed-width signed and unsigned operations when reproducing results in JavaScript.
An integer and a byte sequence can share the same hex spelling but require different parsing, grouping, and text-decoding rules.
Open the Hex Converter →Frequently compared values
Common binary, decimal, hex, and octal values
These reference rows cover the values that appear most often in bit fields, color codes, subnet masks, and file-size math. Grouping is decorative: 11 1110 1000 and 1111101000 are the same number.
00011110221015510008101010A121111F171 0000102010 0000204011 11113F77100 000040100110 010064144111 11117F1771000 0000802001100 1000C83101111 1111FF3771 0000 000010040010 0000 0000200100011 1110 10003E81750100 0000 000040020001000 0000 000080040001111 1111 1111FFF77771 0000 0000 00001000100001111 1111 1111 1111FFFF1777771 0000 0000 0000 000010000200000Powers of two anchor the same table. Each power's binary spelling is a single 1 followed by zeroes, and its hex spelling ends in round steps: 28 = 256 = 100, 212 = 4096 = 1000, 216 = 65536 = 10000. Maxima such as 255, 4095, and 65535 are one power minus one, which is why every digit is F in hex and 1 in binary.
Understand the arithmetic
Convert decimal 203 by hand, then verify it here
Repeated division by 2 produces binary digits from least to most significant. For 203: divide by 2 and keep the remainders — 203 ÷ 2 = 101 remainder 1, 101 ÷ 2 = 50 remainder 1, 50 ÷ 2 = 25 remainder 0, 25 ÷ 2 = 12 remainder 1, 12 ÷ 2 = 6 remainder 0, 6 ÷ 2 = 3 remainder 0, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1. Reading the remainders bottom-up gives 11001011.
Hexadecimal falls out of the same digits in one step. Split 11001011 into 4-bit nibbles — 1100 = 12 = C and 1011 = 11 = B — for CB. Octal groups 3 bits: 11 001 011 = 313. All three spellings describe the same value as decimal 203, which is exactly the cross-check this converter automates.
The same nibble rule runs in reverse: expand each hex digit to 4 bits (3E8 → 0011 1110 1000) to read binary straight off a hex identifier. This is why memory dumps, color codes, and error codes mix hex and binary so freely.
Characters have code points that map to bytes; the ASCII table lists them, and the translator spells them out in binary words.
Open the ASCII Table →Questions answered
Binary converter FAQ
What does a binary converter convert?
This binary converter changes one exact integer value among binary, octal, decimal, and hexadecimal notation. It changes the numeral representation, not the mathematical value, and it does not translate a bit stream into text.
Is binary 10 the same value as decimal 10?
No. The digits 10 in base 2 represent decimal 2, while the digits 10 in base 10 represent decimal 10. Select or prefix the source base before conversion so the same spelling is not interpreted in the wrong radix.
How are negative binary numbers handled?
A leading minus sign represents a mathematical negative integer. A fixed-width bit pattern can instead be interpreted as signed two's complement only after you choose its width. The tool keeps those two meanings explicit rather than guessing.
Why do leading zeroes matter?
Leading zeroes do not change an unsigned mathematical value, but they do record a chosen field or byte width. Preserve or add padding when matching a register, protocol field, test vector, or fixed-width code literal.
Does the binary converter support fractions?
No. This tool intentionally accepts whole numbers. Fractions in another base can repeat forever and require an explicit precision and rounding contract, so they are outside this converter's scope.
Is my number uploaded for conversion?
No. Conversion runs in the current browser tab and does not send the entered value to a number-conversion API. The bounded input limit shown in the interface protects browser responsiveness; clipboard tools and extensions remain separate privacy boundaries.