Odious Number Checker

Odious integer has odd count of1bits in unsigned binary, zero even/not odious; arithmetic uses full safe integer not32bit truncation.

Description

An odious integer has an odd number of one bits in its unsigned binary representation.

An odious integer has an odd number of one bits in its unsigned binary representation.^[1]

This tool counts all bits of a nonnegative safe integer without truncating to a 32-bit bitwise value.

When to use Odious Number Checker

This tool counts all bits of a nonnegative safe integer without truncating to a 32-bit bitwise value.

How to use Odious Number Checker and how it works

Prepare nonnegative safe integer, using the input definitions and matching units below.
Enter the required fields and run Odious Number Checker.
Read result.isOdious, result.binaryOneBitCount using the units, signs and ordering explained below.
Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.

Input field	Meaning	Value type	Requirement
actualNonnegativeSafeInteger	Actual Nonnegative Safe Integer. Use the units and matching context stated in the calculation below.	number	Required; finite; other constraints below

Require a nonnegative safe integer. Convert its full unsigned value to a binary string, count one bits and return the count and whether it is odd. Zero has no one bits and is not odious. No 32-bit bitwise truncation occurs.

oneBits=countOnes(binary(integer)); isOdious=(oneBits mod 2)==1

Apply the input ordering, units and branch conditions stated above.

Output field	Meaning	Value type
result	Object containing the calculated or selected fields below.	object
result.isOdious	True when the full safe-integer binary representation has an odd one-bit count.	boolean
result.binaryOneBitCount	Number of one bits without 32-bit truncation.	number

json

{
  "input": {
    "actualNonnegativeSafeInteger": 7
  },
  "output": {
    "result": {
      "isOdious": true,
      "binaryOneBitCount": 3
    }
  }
}

Limitations and assumptions

The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.

All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.

Alternative or Complementary methods

Use Perfect Digital Invariant Checker for a complementary operation: A perfect digital invariant equals the sum of its decimal digits raised to a specified fixed power.

Use Hyperfactorion Checker for a complementary operation: A hyperfactorion equals the sum of the hyperfactorials of its decimal digits, with the zero-digit empty product equal to one.

References

Odious Number Checker — tool.io

Similar or alternative tools

Perfect Digital Invariant Checker
A perfect digital invariant equals the sum of its decimal digits raised to a specified fixed power.
Hyperfactorion Checker
A hyperfactorion equals the sum of the hyperfactorials of its decimal digits, with the zero-digit empty product equal to one.