8 Bit Floating Point Calculator

Calculator Inputs

Calculation mode

Decimal input

8 bit binary pattern

Exponent bits

Bias mode

Custom bias

Rounding mode

Subnormal support

Infinity and NaN patterns

Formula Used

For a normal value, the calculator uses this formula:

Value = (-1)^sign × (1 + mantissa / 2^{fraction bits}) × 2^{exponent field - bias}

For a subnormal value, the hidden leading one is removed:

Value = (-1)^sign × (mantissa / 2^{fraction bits}) × 2^{1 - bias}

The sign field takes one bit. The exponent and mantissa share the remaining seven bits. The selected exponent width controls the available precision and range.

How To Use This Calculator

Select decimal encoding or binary decoding.
Enter a decimal number or an eight digit binary pattern.
Choose exponent bits. Mantissa bits update from that choice.
Use auto bias, or enter a custom bias value.
Select rounding, subnormal, and special value rules.
Press calculate. The result appears above the form.
Use CSV or PDF export to save the result.

Example Data Table

Decimal	Format	Bias	Binary byte	Hex	Decoded value	Note
0.5	E4M3	7	00110000	0x30	0.5	Exact normal value
1	E4M3	7	00111000	0x38	1	Hidden one is used
-2.5	E4M3	7	11000010	0xC2	-2.5	Negative normal value
10	E4M3	7	01010010	0x52	10	Scaled by exponent
0.015625	E4M3	7	00001000	0x08	0.015625	Smallest normal value

8 Bit Floating Point Guide

What This Calculator Does

Eight bit floating point numbers are tiny numeric formats. They store a sign, an exponent, and a fraction. The small size makes them useful for lessons, experiments, and low precision machine learning demos. This calculator lets you encode a decimal value or decode an existing bit pattern. You can change exponent bits, bias, rounding mode, subnormal handling, and special value support. That makes the tool flexible for many classroom and testing cases.

Why The Format Matters

A floating point value is not stored like a normal integer. It is scaled by a power of two. The exponent chooses that scale. The fraction stores the leading precision. With only eight bits, every bit has strong impact. More exponent bits give a wider range. More fraction bits give better precision. This tradeoff is the main lesson behind the format.

Rounding And Error

Most decimal values cannot fit exactly. The calculator rounds the scaled significand. It can use nearest even, toward zero, floor, or ceiling. After rounding, the decoded value is compared with the original value. The absolute error shows the real difference. Relative error shows the difference against the input size. These outputs help explain why small formats lose detail.

Special Cases

The tool can reserve the all ones exponent for infinity and NaN. This follows the usual floating point idea. It can also allow subnormal numbers. Subnormals keep small values from dropping straight to zero. They use an exponent field of zero and no hidden leading one.

How To Use The Results

Read the sign bit first. Then check the exponent field. Finally review the mantissa field. The binary byte and hex value show the stored code. The decoded value shows what the byte means. The steps explain the scaling process. Use the example table to compare common patterns. Export the result when you need records for notes, tests, or reports.

Practical Tips

Choose four exponent bits and three fraction bits for a balanced example. Increase exponent bits when range matters more. Increase fraction bits when precision matters more. Use nearest even for general work. Use other rounding modes to study edge behavior. Always compare the encoded value with the decoded value.

FAQs

What is an 8 bit floating point number?

It is a compact floating format using eight total bits. One bit stores the sign. The remaining bits store exponent and mantissa fields. This calculator lets you choose that split.

What does E4M3 mean?

E4M3 means four exponent bits and three mantissa bits. With one sign bit, the total becomes eight bits. It is a common teaching layout.

Why does the decoded value differ from my input?

Eight bits cannot represent most decimal values exactly. The calculator rounds the value to the nearest available code or another selected rounding direction.

What is the bias value?

Bias shifts signed exponents into an unsigned stored field. Auto bias uses 2 raised to exponent bits minus one, then subtracts one.

What are subnormal numbers?

Subnormal numbers represent tiny values below the normal range. They use exponent field zero and do not use the hidden leading one.

When is infinity produced?

Infinity appears when special values are enabled and a decimal input overflows the finite range. The exponent field becomes all ones, and mantissa becomes zero.

Can I decode a binary byte?

Yes. Choose the decode mode, enter exactly eight binary digits, and select the same exponent, bias, subnormal, and special value settings.

Which rounding mode should I use?

Nearest even is best for general numeric work. Toward zero, floor, and ceiling are useful for studying boundaries and directed rounding behavior.