IEEE 754 Binary32 Bit Pattern Calculator
Encode a decimal value as a binary32 pattern or decode a 32-bit hexadecimal word, including signed zero, subnormals and special values.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use the binary32 encoding to separate sign, biased exponent and stored fraction. Reconstruct the finite value as an exact rational from those fields.
Normal: (−1)^s(1+f/2²³)2^(e−127); subnormal: (−1)^s f2⁻¹⁴⁹
Worked example
1.5 encodes as 0x3FC00000: sign 0, exponent 127 and fraction 4194304. Hex 00000001 is the smallest positive subnormal, exactly 1/2^149.
Assumptions and input details
Hex words have eight digits with an optional 0x prefix and are displayed in most-significant-byte-first order. Decimal input is first parsed as JavaScript binary64, then rounded to binary32, so extremely rare halfway decimal cases can reflect this two-stage conversion. Explicit NaN, Infinity and -Infinity are accepted in decimal mode. Finite overflow can become infinity. Special values are labelled rather than used in arithmetic. The exact rational comes from the final bit pattern; signed zero is separately identified.
References: Oracle: IEEE arithmetic and single format
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
The decoded sign, exponent, fraction and finite rational value are exact for the final binary32 word. Decimal encoding first parses to JavaScript binary64 and then rounds to binary32; decimal displays and input differences follow that convention.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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