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Information Unit One Bit Reference

Convert an explicit signed information quantity from bits to nats and hartleys without rounding.

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Description

Convert a supplied bit quantity to nats and hartleys.

Information quantities depend on the logarithm base, event model and symbol accounting. Bits, nats and hartleys are logarithmic units, while source symbols, channel symbols and header bits describe different counting bases. A local mass residual or expansion factor does not estimate entropy, independence or channel capacity from data.

Convert a supplied bit quantity to nats and hartleys.

When to use this tool

Use Information Unit One Bit Reference when you already have bits and need to convert a supplied bit quantity to nats and hartleys.

How to use the tool and how it works

  1. Enter bits. Use the units and conventions below.
  2. Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
  3. Read nats, hartleys. Use the output convention below.

Return bits*ln(2) as nats and bits*ln(2)*log10(e) as hartleys.1

Changing the logarithm base changes the information unit. This tool converts a supplied quantity between base-2, natural and base-10 scales without estimating information from observations.2

Input fieldMeaning and unitsAccepted input
bitsSigned quantity on a base-2 information scale; converted as a unit quantity, not calculated entropy.Required. Finite number.
Output fieldInterpretationReturned shape
natsbits*ln(2), using natural-logarithm units.Required. Finite number.
hartleysbits*log10(2), using base-10 units.Required. Finite number.
json
{
  "input": {
    "bits": 1
  },
  "output": {
    "nats": 0.6931471805599453,
    "hartleys": 0.3010299956639812
  }
}

Limitations and assumptions

  • Signed inputs are allowed; this converts logarithmic units without computing entropy, information content, a code length or a valid probability model.
  • Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
  • Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.

Alternative or Complementary methods

Evaluate the full probability model, code and payload/header format when studying information or efficiency. Keep symbol and logarithm bases explicit; a unit conversion or one joint-mass reference term is only a local calculation.

References

  1. Calculation and input contract: information/information-unit-one-bit-reference — tool.io

  2. A Mathematical Theory of Communication (1948) — Claude E. Shannon

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