Configure the fixed-point conversion
Use automatic midpoint bias for standard offset binary.
Example data table
| Value | Format | Scaled integer | Bias | Offset binary | Decoded value |
|---|---|---|---|---|---|
| -0.75 | 8 bits, 4 fraction bits | -12 | 128 | 0111 0100 |
-0.75 |
| 0 | 8 bits, 4 fraction bits | 0 | 128 | 1000 0000 |
0 |
| 1.375 | 8 bits, 4 fraction bits | 22 | 128 | 1001 0110 |
1.375 |
| 0.3125 | 8 bits, 4 fraction bits | 5 | 128 | 1000 0101 |
0.3125 |
Understanding fractional offset binary
Fractional offset binary stores signed fixed-point values in an unsigned bit pattern. It is also called biased binary. The representation moves zero near the middle of the available codes. Negative values occupy lower codes. Positive values occupy higher codes. It is useful for converters, sensors, and digital signal paths. The displayed fractional value needs a chosen binary scale. Fraction bits define that scale. More fraction bits create smaller value steps. Total bits determine the full storage range. The calculator makes these choices visible before encoding your value.
How conversion works
The conversion starts by scaling the input. Multiply the decimal value by two raised to fractional bits. This produces the signed fixed-point integer. The selected rounding rule then removes any remaining fraction. Nearest rounding uses the closest integer. Truncation removes digits toward zero. Next, add the selected bias. Automatic bias equals two raised to total bits minus one. The resulting unsigned integer becomes the stored offset-binary code. It subtracts the bias and divides by the scale. This confirms the representable value after quantization.
Formula used
Scaled integer = quantize(value × 2F)
Encoded integer = scaled integer + bias
Decoded value = (encoded integer − bias) ÷ 2F
Automatic bias = 2N − 1
Use the following relationship for the calculation. Scaled integer equals quantize(value multiplied by two to F). Encoded integer equals scaled integer plus bias. Decoded value equals encoded integer minus bias, divided by two to F. Here, F means the number of fractional bits. For automatic bias, bias equals two to N minus one. Here, N means the total number of stored bits. The least significant bit equals one divided by two to F. This value is the smallest available step.
Precision, rounding, and range
Rounding affects precision. A number exactly between steps requires a rule. Nearest rounding usually reduces total error. Truncation is useful when hardware discards extra bits. The result panel shows the quantization error. It also shows the allowed input range. Select more bits when range is insufficient. Select more fraction bits when smaller changes matter. Remember that more fractional bits reduce integer range. Check the decoded value before saving a code.
How to use this calculator
Begin by entering a signed decimal value. Then select the total stored bit width. Choose fractional bits for your required resolution. Select automatic or custom bias. Automatic bias follows the standard midpoint arrangement. Use custom bias only for a known device format. Choose the rounding method. Select a grouping style for easier code reading. Press Convert to see the code above the form. Review range, scale, encoded integer, and decoded value. Copy the bit string or download the shown result.
Practical uses and checks
Offset binary is common in analog-to-digital output formats. It also appears in communication and measurement equipment. Many systems place zero at the midpoint code. The most significant bit changes across the midpoint. With automatic bias, offset binary matches two's complement after flipping that bit. This comparison can help during debugging. Always confirm a device's documented bit order. Confirm whether its input is normalized or fixed-point. Confirm the required bias before transmitting any code. Small differences can change output bits.
Frequently asked questions
What is offset binary?
Offset binary stores a signed value after adding a bias. The stored bits are therefore unsigned. The midpoint code usually represents zero.
Why are fraction bits needed?
Fraction bits create fixed-point precision. Each extra fraction bit halves the smallest available step. They also reduce the available whole-number range.
What does automatic midpoint bias mean?
Automatic midpoint bias uses 2 raised to N minus one. N is the total bit count. This is the usual offset-binary arrangement.
Can I enter negative fractions?
Yes. Enter a minus sign before the decimal value. The calculator checks whether the quantized value fits the selected format.
What does nearest rounding do?
Nearest rounding selects the closest scaled integer. Exact half steps move away from zero. This often reduces the visible conversion error.
When should I use truncation?
Use truncation when your target hardware simply discards lower fractional bits. It removes the scaled fraction toward zero.
Why does the decoded value differ?
The selected format may not represent every decimal value exactly. Scaling and rounding create the nearest available fixed-point value.
How is offset binary related to two's complement?
With standard midpoint bias, flip the leading bit of a two's-complement pattern. The result is the matching offset-binary pattern.
Can custom bias be useful?
Yes. Some instruments use documented nonstandard bias values. Enter that value only when the device specification requires it.
What bit widths are supported?
The calculator supports two through fifty-two total bits. This keeps calculations reliable with standard server-side numeric values.
Does bit grouping change the result?
No. Grouping adds spaces only for readability. The raw bit string remains unchanged and is used for copying and exports.