Apple Numbers XOR: Odd-Parity Logic and Exactly-One Checks

• Introduced: The original release and introduction date are not established by the checked references.
• Availability: Currently documented in Apple’s Functions Help 15.4 documentation edition. No final supported-version endpoint is established.
• Scope: Shared iWork reference; exact historical availability in individual Mac, iPad, iPhone and iCloud builds remains unverified.
• Checked: October 14, 2026, against the official XOR reference. Examples checked by independent boolean logic; no native Numbers test.

=XOR(any-expression, any-expression…)

One expression is required; additional expressions are optional. Each must be evaluable as a boolean. Apple states that numeric 0 is false, while every nonzero number is true. Negative numbers therefore count as true when passed directly, even if a separate test such as A2>0 would be false.

XOR differs from OR, which accepts any true condition, and AND, which requires every condition to be true. It returns a boolean result, not a count of successful conditions.

For two boolean inputs, XOR means exactly one is true. That description becomes incomplete for three or more inputs. Use a count-equals-one test when the business rule is genuinely one choice out of many.

Create a Numbers table named TruthTable, with seven columns A:G and nine rows including one header row. Put First, Second, Third, XOR, OR, AND and Exactly one in A1:G1. Enter the following eight combinations in A2:C9 as unquoted TRUE/FALSE values:

Enter these formulas in row 2 and fill D2:G2 through row 9:

• D2: =XOR(A2,B2,C2)
• E2: =OR(A2,B2,C2)
• F2: =AND(A2,B2,C2)
• G2: =(IF(A2,1,0)+IF(B2,1,0)+IF(C2,1,0))=1

The G formula explicitly converts each condition to a count contribution, then asks whether their sum is one. Row 9 exposes the difference: XOR returns TRUE for three true values, while Exactly one returns FALSE.

Create another table named NumericControls, with two columns A:B and seven rows. Put these formulas in B2:B7, with a descriptive label alongside each:

In B3 the number −2 is itself a true logical input. In B7 the comparison −2>0 is false. Write the condition that actually represents your rule instead of relying on an unintended numeric conversion.

The entry does not give a complete rule table for arbitrary text, error cells, blank references or array coercions. These controls use scalar numbers and explicit comparisons only.

Create a separate table named DeliveryChoice, with five columns A:E and five rows. Use Pickup, Courier, One method, Message and Algebra check as headers. Enter A2:B5 as:

Enter =XOR(A2,B2) in C2, =IF(C2,"Ready","Choose one method") in D2 and =AND(OR(A2,B2),NOT(AND(A2,B2))) in E2. Fill C2:E2 through row 5.

The E formula independently expresses the same two-choice rule: at least one is true, and both are not true. With two valid booleans it agrees with XOR in all four cases.

If you add a third delivery option later, do not simply append it to XOR and assume the rule still means exactly one. Use the count test demonstrated in TruthTable instead. Keep a visible all-selected control so that this mistake is easy to detect.

A TRUE result does not identify which condition was true. Retain the original columns when you need to explain a decision. Similarly, XOR cannot validate whether your source inputs were complete or whether a text label was intended as a boolean.

Use IF to turn the result into a label, or NOT to reverse a valid boolean result. The TRUE and FALSE functions provide explicit constants for reproducible controls. XOR’s short reference does not establish every exact native error token or historical build boundary.