# 3-input XOR gate truth table

Given the truth table for a 3-input XOR, how come the output is 1 when all inputs are 1? This doesn't logically extend from a 2-input XOR where output is 0 when all inputs are 1. Is there a way to understand this intuitively, or do we need kmaps etc?

(source: electronicshub.org)

• Commented Jan 16, 2017 at 16:22
• Always remember XOR is an odd parity detector, For example an XOR with N inputs will output 1 if only odd number of inputs is asserted Commented Jan 16, 2017 at 16:31
• @Elbehery It depends on the definition. And apparently it is ambiguous as the answer in the link above is describing. Commented Jan 16, 2017 at 17:00
• There are two definitions for XOR: just one injput is high, or a odd number of inputs is high. For 2 inputs these definitions coincide, for more than two inputs the world seems to be divide 50-50. Commented Jan 16, 2017 at 18:03
• A niche little trick to remember this can be odd number of ones give the output one. This trick works with any number of inputs! Commented Jan 28 at 9:21

It may help to break it down: first do $A \oplus B = 1 \oplus 1 = 0$. Then we have $0 \oplus C = 0 \oplus 1 = 1$.