If you need a fast way to convert between decimal numbers and IEEE 754 binary floating-point format, this iee754 calculator gives you both directions in one place. It supports 32-bit single precision and 64-bit double precision, and breaks the value into sign, exponent, and fraction fields so you can clearly see what is happening.
Decimal → IEEE 754
IEEE 754 → Decimal
What is IEEE 754?
IEEE 754 is the standard most computers use to store floating-point numbers. Instead of saving every decimal exactly, it stores numbers using a binary scientific notation format. That gives very wide range and fast performance, but it also introduces rounding behavior that developers must understand.
- Single precision (32-bit): 1 sign bit, 8 exponent bits, 23 fraction bits.
- Double precision (64-bit): 1 sign bit, 11 exponent bits, 52 fraction bits.
- Special values: ±0, subnormals, ±Infinity, and NaN.
How to use this iee754 calculator
1) Convert decimal to IEEE 754
Type a decimal value such as 13.25, -0.75, or 0.1. Choose 32-bit or 64-bit. The result shows full binary, hexadecimal form, and each field (sign, exponent, fraction).
2) Decode IEEE 754 back to decimal
Paste either binary bits or hex (for example, 0x3F800000). Select precision, then decode. The tool reconstructs the decimal value and reports the number class.
Understanding the three fields
Sign bit
The sign bit is simple: 0 means positive, 1 means negative.
Exponent field
The exponent is stored with a bias. For single precision, the bias is 127. For double precision, the bias is 1023. A stored exponent of all zeros or all ones signals special handling (subnormals, zero, infinity, NaN).
Fraction (mantissa) field
The fraction stores the significant digits in binary. For normalized values, there is an implicit leading 1 before the fraction bits. For subnormal values, that implicit bit is 0, which allows representing tiny numbers close to zero.
Why floating-point surprises happen
Some decimals cannot be represented exactly in binary. The classic example is 0.1. In IEEE 754, it is rounded to the nearest representable binary value. This is why expressions like 0.1 + 0.2 may not display exactly 0.3 in many languages.
Common practical takeaways
- Use tolerance comparisons for floating-point equality checks.
- Prefer decimal/fixed-point types for money calculations.
- Know the precision limits of 32-bit vs 64-bit floats.
- Use tools like this calculator when debugging serialization and bit-level data exchange.
Special values in IEEE 754
- Zero: exponent all 0s and fraction all 0s (sign decides +0 or -0).
- Subnormal: exponent all 0s and fraction not all 0s.
- Infinity: exponent all 1s and fraction all 0s.
- NaN: exponent all 1s and fraction not all 0s.
When this calculator is useful
This IEEE 754 converter is useful for low-level debugging, protocol design, binary file inspection, compiler coursework, and numerical software development. If you work with embedded systems, graphics pipelines, scientific code, or data formats, bit-level visibility is essential.