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IEEE-754 Floating Point Converter

Convert decimal, hexadecimal, or raw bits for IEEE 754 binary32 and binary64, then inspect exact stored values, rounding error, exponent fields, special values, and byte order.

Decimal ↔ hex ↔ bitsbinary32 and binary64 raw words

Exact stored valuesee the decimal value the bits actually encode

Rounding error + ULPmeasure representation error instead of hiding it

Byte order + special valuesinspect ±0, subnormals, infinities and NaNs

Direction

Precision

Input

—Uses the browser's Float32/Float64 binary representation.

—sign

—exponent bits

—classification

—hex bits

Check the number representation

Keep number base, bit width, signedness and byte order explicit instead of letting one representation silently imply another.

ParseIdentify the input base or prefix before calculation.

RepresentCross-check binary, octal, decimal and hexadecimal views.

CalculateUse arithmetic or bitwise operations with exact integer scope.

Inspect bitsChoose width, signed interpretation, shifts and byte order explicitly.

Copy / verifyCopy only after checking the representation your code or protocol expects.

Base arithmetic Binary calc Hex calc Bitwise Shift Signed/unsigned Two’s complement Endian

All developer-number calculations run locally. Fixed-width tools model integer bit patterns, not language-specific undefined behavior, CPU flags, binary protocol schemas or floating-point reinterpretation unless a dedicated tool says so.

IEEE 754 floating-point inspector

See the bits, exact value, and rounding error

Encode a decimal or decode a raw hexadecimal/binary word. The inspector separates sign, exponent and fraction fields, then reconstructs the exact finite value with integer arithmetic.

binary32 · binary64 · browser-local

Input typePrecisionValue

Raw bit fields

■ sign■ exponent■ fraction / mantissa field

normalclassification

—canonical hex word

—biased exponent field

—unbiased exponent

—exponent bias

—significand form

Exact value and spacing

Exact stored decimal

—stored − typed

—relative error

—ULP / local spacing

—adjacent lower encoding

—adjacent higher encoding

Byte-order view

Big-endian bytes
—

Little-endian bytes
—

The canonical hex word keeps the most-significant byte first. Memory byte order is a separate choice, so both byte sequences are shown explicitly.

Copyable IEEE 754 audit

Ready.

Precision boundary. This workspace covers IEEE 754 binary32 and binary64 with the browser's normal round-to-nearest behavior. A raw NaN word preserves its payload bits for inspection; JavaScript arithmetic may canonicalize NaNs. The hex word is a numeric bit pattern, while big-endian/little-endian rows describe byte order in memory or protocols. “Mantissa” is commonly used for the stored fraction field; the numerical significand includes the implicit leading 1 for normal values.

IEEE 754 bit-field & rounding audit

Keep the existing decimal/hex/binary converter, then expose the unbiased exponent, significand field, exact stored value and ULP spacing.

Exact stored value

Exact stored value

—

Spacing / precision

—

The exact stored binary value can differ from the decimal text you typed; binary32 makes that especially visible.

Representation is context

A hexadecimal or binary string does not automatically tell you whether a value is signed, how wide it is, whether bytes are little endian, or whether the bits represent an integer or floating-point value.