Tools

IEEE 754 Float Analyzer

See how a decimal number is actually stored in floating point. The bit field is split into sign , exponent and mantissa for both 32-bit and 64-bit precision, with the exact stored value and its rounding error.

Try

Input

0.1

Classification

finite

Denormal (32-bit)

Denormal (64-bit)

Representationsbits run most-significant first; 0 bits are dimmed

Sign Exponent Mantissa

32-bit Single Precision (32-bit)rounded

Sign1 bit

Exponent8 bits

0111101

Mantissa25 bits

1 10011001100110011001100

Hex

0x0E3333330

Binary

0 01111011 10011001100110011001100

Sign

positive

Stored exp

123

01111011

Actual exp

-4

stored − 127

Bias

127

8 exponent bits

Exact stored value

0.099999994039535522

rounding error -5.960464e-9

64-bit Double Precision (64-bit)exact

Sign1 bit

Exponent11 bits

0111111101

Mantissa54 bits

1 1001100110011001100110011001100110011001100110011010

Hex

0x0FD16666666666662

Binary

0 01111111011 1001100110011001100110011001100110011001100110011010

Sign

positive

Stored exp

1019

01111111011

Actual exp

-4

stored − 1023

Bias

1023

11 exponent bits

Exact stored value

0.10000000000000001

represented exactly — no rounding error