IEEE 754 Floating-Point Visualizer & Converter

Convert 32-bit single and 64-bit double precision floats into Sign bit, Exponent, Mantissa, and Hexadecimal representations.

IEEE 754 Floating-Point Visualizer & Converter

Convert 32-bit single and 64-bit double precision floats into Sign bit, Exponent, Mantissa, and Hexadecimal representations.

Decimal Float Value:

Precision Format:

Binary Bit Fields (32-bit):

00111101110011001100110011001101

■ Sign (1 bit)■ Exponent (8 bits)■ Mantissa (23 bits)

Hex Representation:

0x3DCCCCCD

Unbiased Exponent (2^n):

2^-4

Actual Stored Float:

0.10000000149011612

About This Tool

The IEEE 754 Floating-Point Visualizer converts decimal numbers into their exact 32-bit Single Precision (float) and 64-bit Double Precision (double) binary bit fields (Sign, Exponent, Mantissa/Fraction).

Key Features

32-bit Single Precision and 64-bit Double Precision support

Interactive color-coded bit field visualization (Sign, Biased Exponent, Mantissa)

Handles special values: Infinity, -Infinity, NaN, and Subnormal numbers

Hexadecimal memory word inspection

How to Use This Tool

Enter any decimal float value (e.g. 0.1, -15.625, 3.14159).
Select precision mode: 32-bit Single or 64-bit Double.
Inspect the color-coded Sign bit, Exponent, Fraction bits, and actual stored value.

Why Use This Tool

Understand why `0.1 + 0.2 !== 0.3` in JavaScript and Python due to IEEE 754 binary rounding.
Debug graphics shader precision and embedded microcontroller float math.
Verify floating-point serialization protocols.

Pro Tips

The exponent uses a bias (127 for 32-bit, 1023 for 64-bit) to represent both positive and negative powers of 2 without a separate sign bit.

Frequently Asked Questions

How does IEEE 754 represent floating-point numbers?

IEEE 754 divides binary numbers into three parts: 1 sign bit, an exponent field with a fixed bias (127 for 32-bit, 1023 for 64-bit), and a fractional mantissa.

Why does 0.1 + 0.2 not equal 0.3 in JavaScript?

In base-2 binary floating point, 0.1 and 0.2 are infinite repeating fractions, leading to minor rounding errors at the 53rd bit of precision (0.30000000000000004).

IEEE 754 Floating-Point Visualizer & Converter