Floating Point Internals

An interactive visualization of how computers store decimal numbers using the IEEE 754 Single-Precision standard. Toggle the bits to see how the sign, exponent, and mantissa affect the final value.

IEEE 754 Visualizer

32-BIT SINGLE PRECISION FLOAT

VALUE:

EXPONENT (8)

MANTISSA (23)

SIGN BIT Positive (0)

EXPONENT 0 (denormalized or zero)

HEX REPRESENTATION 0x00000000

UNDER THE HOOD

Memory Allocation: 32 bits (4 bytes)

Structure:

Bit 31: Sign (0=Positive, 1=Negative)
Bits 30-23: Exponent (Bias 127)
Bits 22-0: Mantissa (Fractional part)

// Formula

Value = (-1)ˢ × 1.m × 2⁽ᵉ⁻¹²⁷⁾