Compare Signal Rules: Another Case

Use fresh input pairs to explain neither, not both and matching values.

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Watch the lesson | Practice 1: neither and matching

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Use Boolean 0 and 1 only. Inclusive OR accepts either or both ones; AND needs both ones. NOR = NOT (A OR B), NAND = NOT (A AND B), and XNOR = NOT (A XOR B). Two-input XOR accepts different values. Compare complete rules using 00, 01, 10 and 11; one differing row disproves equivalence. These are ideal rules for paper or screen, not real voltages or wiring.

Worked example

At A = 1 and B = 0, XOR is 1, so XNOR is 0. At 1 and 1, XOR is 0, so XNOR is 1. Matching is about equality, not how many inputs are switched on.

XNOR accepts both matching pairs, 00 and 11. AND misses 00 even though those zeros match. — A matching-values rule must also accept two zeros. Use the operation definitions to explain each row.

Would you believe it?

Different triples can have the same odd-parity value: 001 and 010 each contain one 1. Two positions differ, yet both parity outputs are 1. Matching parity alone does not prove matching data.

Texas Instruments: three-input XOR function table

Question 1 At A = 1 and B = 0, what is NOR? 1 0 2

Question 2 At A = 1 and B = 0, which result pair is correct: NAND, then NOR? 0, 1 1, 1 1, 0

Question 3 At A = 0 and B = 1, what is XNOR? 0 1 2

Question 4 A matching-values sign uses AND. Which input pair proves the design wrong? 01 11 00

Question 5 Two Boolean rules disagree at 10 but agree at 00, 01 and 11. Are they equivalent? Yes; three matching rows outvote one. No; one differing row is enough to disprove equivalence. Only if the differing output is 0.

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