IEEE 754 binary32 and binary64 bit visualizer
Explore binary32 and binary64 floating-point bits, bias, exact stored decimal values, signed zero, infinity and a fixed quiet NaN locally.
About this ieee 754 binary32 and binary64 bit visualizer
Explore binary32 and binary64 floating-point bits, bias, exact stored decimal values, signed zero, infinity and a fixed quiet NaN locally Computes exact algebraic and numerical metrics directly in your browser using IEEE 754 precision without round-trip latency.
Formula & calculation mechanics
Enter a decimal or choose a special value. Inspect both formats, colored sign/exponent/fraction bits, hexadecimal and restored values. Open the exact decimal section for the full stored value.
Worked numerical calculation
Scenario: Example: 0.1
Sample input:
Processing: DataView.setFloat64 stores the parsed number; emit sign bit 0, bits 1–11 as exponent, and the remaining 52 as fraction.
Illustrative output:
Domain range & precision boundaries
Operational constraints and validation boundaries: Input first rounds to JavaScript binary64, then binary32 rounds that value to nearest, ties to even. This is not a direct arbitrary-precision decimal-to-binary32 converter. Up to 128 characters; finite binary64 input required. Very small decimals can round to signed zero; binary32 can overflow to infinity. Hex order is a display convention, not machine byte order.
Calculations in IEEE 754 binary32 and binary64 bit visualizer use standard IEEE 754 precision or exact rational models. Verify significant accounting or tax figures with authoritative references.
In-browser calculation boundary
Formula calculations and numeric evaluations in IEEE 754 binary32 and binary64 bit visualizer run synchronously in the browser JavaScript engine with zero server telemetry.
Mathematical formulas & precision standards
Mathematical constants, IEEE 754 floating-point standards, and numerical analysis specifications:
IEEE 754 binary32 and binary64 bit visualizer verification · Audit standards
How to use it
- Enter, paste, or select your input data into the IEEE 754 binary32 and binary64 bit visualizer workspace controls.
- Review parameter fields, units, or options configured for IEEE 754 binary32 and binary64 bit visualizer.
- Click the action button or observe immediate live calculations rendered by IEEE 754 binary32 and binary64 bit visualizer.
IEEE 754 Floating-Point Representation, Bit-Level Layout, and Rounding Hazards →
A deep technical analysis of IEEE 754 binary32 and binary64 specifications, sign-exponent-mantissa bit layouts, subnormal numbers, and floating-point arithmetic traps.
Frequently asked questions
How does IEEE 754 Floating-Point Visualizer configure exponent?+
Normal: (−1)^s × 2^(E−bias) × 1.f; subnormal: (−1)^s × 2^(1−bias) × 0.f. Bias is 127 / 1023; fraction has 23 / 52 stored bits. All-zero exponent with zero fraction means signed zero; all-one exponent means infinity or NaN.
Decimal number+
Input first rounds to JavaScript binary64, then binary32 rounds that value to nearest, ties to even.
Example: 0.1+
In binary64, 0.1 + 0.2 = 0.30000000000000004, while 0.3 has a different bit pattern. Each decimal first rounds to a binary fraction and addition rounds again. This tool displays representations; it does not parse expressions.
How does IEEE 754 Floating-Point Visualizer configure nan?+
The NaN preset uses a fixed quiet-NaN example (0x7fc00000 / 0x7ff8000000000000). It does not inspect arbitrary NaN payloads or signaling NaNs. Signed zeros compare equal but retain different sign bits.