ES
IEEE 754 Floating Point

X-Ray: Binary32

Single Precision (32-bit) Structure

1

1bit Sign

0(+)|1(-)

01111011

8bits Exponent

Bias: 127

10011001100110011001101

23bits [±1.18×10-38, ±3.4×1038] Mantissa / Fraction

Precision bits after the decimal point

Formula:
Actual Value:
-0.1
Stored in Float:
-0.100000001490116119384765625

The Bias

Instead of a signed integer, the exponent uses a bias of 127 to represent both positive and negative powers.

Hidden Bit

To save space, the first digit (1.) is implicit and not stored in the 23 bits of the mantissa.

NaN

Result of undefined operations like 0/0.

Infinity

Exponent all 1s, Mantissa all 0s.

Precision

Approx. 7 decimal digits of accuracy.

Underflow

Numbers too small to be represented.

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1s sign • 8e range • 23m accuracy.