XOR vs OR: inclusive or exclusive?

OR and XOR differ in exactly one row of the truth table. OR (inclusive or) outputs 1 when at least one input is 1, including when both are. XOR (exclusive or) outputs 1 only when the inputs differ, so when both inputs are 1 it outputs 0. In Boolean form, A OR B = A + B, while A XOR B = A'B + AB'. XNOR is the inverse of XOR: it outputs 1 when the inputs are equal. If either input being 1 is enough, it is OR; if it must be one or the other but not both, it is XOR.

What each gate is used for

OR combines conditions: an alarm that sounds when either of two doors opens, an interrupt raised by any of several devices, an address range made of several decodes. XOR detects difference: it is the sum bit of a half adder (1 + 1 = 10, so the sum digit is 0), the heart of parity generators, a controlled inverter (A XOR 1 = NOT A), and, as XNOR, the bit-equality test inside comparators. In CMOS an OR gate is a NOR plus an inverter, 6 transistors; an XOR takes about 8 with transmission gates, or 12 as a fully complementary gate.

Try both live in digiwleea

Toggle the inputs of the live OR gate, XOR gate and XNOR gate, then build them from transistors: the CMOS OR and CMOS XOR, or XOR from four NAND gates. The XOR lesson explains why XOR needs more transistors than OR.

OR, XOR and XNOR truth table

A	B	A OR B	A XOR B	A XNOR B
0	0	0	0	1
0	1	1	1	0
1	0	1	1	0
1	1	1	0	1

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More comparisons: Digital logic concepts compared

Relay vs transistor Assembly vs machine code MOSFET vs BJT Assembler vs compiler Ladder logic vs logic gates Half adder vs full adder ASCII vs Unicode NAND vs NOR KB vs KiB Encoder vs decoder Bit vs byte PAL vs PLA

See for yourself: build a logic gate from transistors in the simulator, then follow the path from sand to an 8-bit CPU.

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Frequently asked

What is the difference between XOR and OR?

OR outputs 1 when one or both inputs are 1. XOR outputs 1 only when exactly one input is 1, so for inputs 1 and 1, OR gives 1 and XOR gives 0.

What is 1 XOR 1?

0. XOR outputs 1 only when its inputs differ.

Is XOR the same as addition?

For single bits it is addition without the carry: 1 + 1 = 10 in binary, and XOR gives the 0 digit while AND gives the carry, which is exactly a half adder.

What is XNOR?

The inverse of XOR: XNOR outputs 1 when its inputs are equal (both 0 or both 1), so it tests whether two bits match.