Question 1

What does the IEEE 754 converter do?

Accepted Answer

Type a decimal number (or a hex float like 0x1.8p+1) and the tool decomposes it into the IEEE 754 sign / exponent / mantissa bit fields for all four standard widths — binary16 (half), binary32 (single), binary64 (double), and binary128 (quad). You see the raw bit pattern in binary and hex, the field breakdown, the classification (normal / subnormal / ±0 / ±inf / qNaN / sNaN), the exact value actually stored (computed with BigInt so it is correct to the last digit), and the absolute / relative rounding error versus your typed input.

Question 2

How are special values (inf, NaN, subnormals, ±0) handled?

Accepted Answer

All four widths follow the IEEE 754 encoding: an all-ones exponent with a zero mantissa is ±inf, an all-ones exponent with a non-zero mantissa is NaN (most-significant mantissa bit set = qNaN, cleared = sNaN), an all-zero exponent with a non-zero mantissa is a subnormal, and an all-zero exponent with a zero mantissa is ±0 (distinguished by the sign bit). The tool labels each of these explicitly and the clickable bit grid highlights the field boundaries.

Question 3

How does the binary128 path work when JavaScript has no native 128-bit float?

Accepted Answer

binary16 / 32 / 64 use the browser's typed arrays (DataView + Uint16Array / Float32Array / Float64Array) for hardware-exact conversion. For binary128, which has no native JS type, the tool falls back to a BigInt-based path: the decimal input is parsed as an exact rational (numerator / denominator), the nearest representable quad-precision value is computed with round-to-nearest-even, and the exact stored decimal is reconstructed from the bits via BigInt math. It is correct but slower than the hardware paths.

Question 4

What is ULP stepping and hex-float parsing?

Accepted Answer

ULP (unit in the last place) is the gap between two consecutive representable floats at the current exponent. The Next / Previous buttons step the value by exactly one ULP, so you can walk every representable number in the chosen precision. Hex-float parsing accepts the C99 / JS-style literal 0x1.91eb86p+1, where the part before 'p' is a hex fraction and the part after is a binary exponent — useful for copying exact bit patterns out of compiler diagnostics or specs.

Question 5

What extra features does this tool have compared to other IEEE 754 converters?

Accepted Answer

(1) All four widths — binary16, 32, 64, and 128 — in one tool (most only do 32 or 64). (2) Exact stored value to the last digit via BigInt (not a re-printed JS number). (3) Absolute AND relative rounding error displayed side-by-side. (4) Full classification including qNaN vs sNaN and ±0 distinction. (5) Clickable bit grid — toggle any bit and watch every field update. (6) Per-field color coding (sign / exponent / mantissa). (7) Hex-float input parsing (0x1.8p+1). (8) ULP next / previous stepping. (9) Side-by-side precision comparison of the same input across all four widths. (10) Copy fields / hex / binary. (11) History (localStorage, last 20). (12) Shareable URL with full state round-trip. 100% client-side and offline — your numbers never leave the device.

IEEE 754 Floating-Point Converter (binary16 / 32 / 64 / 128)

binary64 (double)

How to use

binary64 (double)