10月31日和12月25日是否是同一天？

There are only 10 types of people in the world: those who understand binary, and those who don't.

This joke relies on the fact that mathematical expressions, just as expressions in natural languages, may have multiple meanings. Like other puns, the humor is derived from an ambiguous meaning; in this case, the expression 10 in the binary numeral system is equal to the decimal number two.

Another pun using different radices, sometimes attributed to computer scientists, asks:

Why do mathematicians always confuse  Halloween and  Christmas?

Because 31  Oct = 25  Dec.

The humor lies in the similarity of the abbreviation for October/Octal and December/Decimal, and the coincidence that the two representations equal the same amount (31 Octal is 3*8 + 1 = 2*10 + 5 = 25 Decimal).