IEEE 754 Floating Point Converter

IEEE 754 stores a sign, a biased exponent and a fraction: −12.375 in single precision is 0xC1460000.

Convert:

Decimal → IEEE 754 bitsHex bits → decimal

Format:

Single (32-bit)Double (64-bit)

Decimal number:

Also accepts NaN, Infinity and scientific notation like 1.5e-3.

IEEE 754 single (hex)

0xC1460000

Sign bit: 1 (negative)
Exponent (8 bits): 10000010 = 130, actual exponent 130 − 127 = 3
Mantissa (23 bits): 10001100000000000000000
All bits: 1 10000010 10001100000000000000000
Class: normal
Value actually stored: -12.375

Step-by-step solution

Value = (−1)^1 × 1.mantissa × 2^(130 − 127)
= −1.100011₂ × 2^3

IEEE 754 Floating Point Converter Formula

value = (−1)ˢ × 1.m × 2^(e − bias)

single: 8-bit exponent, bias 127, 23-bit mantissa; double: 11, 1023, 52

Worked Example

−12.375 in single precision:

Value = (−1)^1 × 1.mantissa × 2^(130 − 127)
= −1.100011₂ × 2^3

Exponent (8 bits): 10000010 = 130, actual exponent 130 − 127 = 3 · Mantissa (23 bits): 10001100000000000000000 · All bits: 1 10000010 10001100000000000000000 · Class: normal · Value actually stored: -12.375

GATE tip

Convert by hand as GATE expects: write the number in binary (12.375 = 1100.011), normalise (1.100011 × 2³), add the bias (3 + 127 = 130 = 10000010) and drop the leading 1 for the mantissa.

More Digital Logic and Number Representation Calculators

Number Base Converter

N = Σ dᵢ·bⁱ

integer part: repeated division; fraction: repeated multiplication by the base

Example: The decimal number 45.625: Binary = 101101.101.

Open the number base converter →
Two’s Complement Calculator

−x = invert(x) + 1

n-bit range −2ⁿ⁻¹ … 2ⁿ⁻¹ − 1

Example: −45 as an 8-bit number: 8-bit two’s complement = 1101 0011.

Open the two’s complement calculator →
K-Map Solver

F = Σm(…) + d(…) → minimal SOP / POS

Quine–McCluskey with an exact minimum cover

Example: F(A, B, C, D) = Σm(0, 1, 2, 5, 6, 7, 8, 9, 10, 14): Minimal SOP: F(A, B, C, D) = B′C′ + CD′ + A′BD.

Open the k-map solver →

Frequently asked questions

What is the exponent bias in IEEE 754?

127 for single precision and 1023 for double; the stored exponent is the true exponent plus the bias.

What are denormal (subnormal) numbers?

Values with an all-zero exponent field and no implied leading 1, which fill the gap between 0 and the smallest normal number.

Sources

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.

Cite this page

APA

Scientific Converters. (2026, October 15). IEEE 754 Floating Point Converter. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/ieee-754-converter/

IEEE

Scientific Converters, "IEEE 754 Floating Point Converter," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/ieee-754-converter/