IEEE 754 浮動小数点エミュレーター

This tool interprets the decimal input as an exact rational number and converts it to IEEE 754 binary32 or binary64. It does not pass through JavaScript number conversion, so you can compare all rounding directions.

Input and format

Decimal valueExamples: 2.35, -0, 1.25e-10, Infinity, NaN

Floating-point format

float (binary32)double (binary64)

Rounding direction for details

Examples:

Bit representation

Nearest, ties to even

0100000000000010110011001100110011001100110011001100110011001101

Sign (1 bit)Exponent (11 bits)Fraction (52 bits)

Hexadecimal

0x4002CCCCCCCCCCCD

ClassificationNormal

Unbiased exponent1

Relation to inputGreater than the input

Stored value

Shortest decimal representation

2.35

Exact decimal value stored after rounding

2.350000000000000088817841970012523233890533447265625

Binary significand

1.0010110011001100110011001100110011001100110011001101

The shortest representation is a compact decimal that round-trips to the same value using round-to-nearest, ties-to-even. The exact stored value is not a repeat of the decimal input: it is the complete decimal value represented by the bit pattern after rounding to the selected format.

Rounding direction comparison

Results for double (binary64) (53 bits of precision). Select a row to show its details.

Rounding direction	Shortest decimal	Relation	Hexadecimal
Nearest, ties to even	`2.35`	Greater than the input	`0x4002CCCCCCCCCCCD`
Nearest, ties away from zero	`2.35`	Greater than the input	`0x4002CCCCCCCCCCCD`
Toward positive infinity	`2.35`	Greater than the input	`0x4002CCCCCCCCCCCD`
Toward negative infinity	`2.3499999999999996`	Less than the input	`0x4002CCCCCCCCCCCC`
Toward zero	`2.3499999999999996`	Less than the input	`0x4002CCCCCCCCCCCC`