Please explain this geek joke!

Question

Please explain this geek joke.

Why do programmers always get Christmas and Halloween mixed up?

Because DEC 25 = OCT 31

How does 1225=1031?

Answer 1

The value of Decimal 25 equals the Octal 31.

Answer 2

Decimal (base 10) number 25 is the same as Octal (base 8) 31

Bert

Answer 3

Octal, is base 8. So 3 * 8 + 1 = 25

Decimal, base 10 is what we use.

So OCT (octal) 31 = DEC (decimal) 25

Definitely a geek joke.

==

Douglas Adams' book, the Hitchhiker's Guide to the Galaxy, the answer to the whole question of Life, the Universe, and Everything turns out to be 42. But the question wasn't really defined.  So the story generates one.  It turns out to be "what is 6 times 9?".  Which isn't 42.  It's 54. But in base 13, 42 is 4 * 13 + 2 = 54.  Adams says that this isn't what he meant. He meant that the Universe doesn't make any sense.  But some geek noticed this anyway.

Answer 4

The idea is that 25 in decimal notation (base 10) equals 31 in octal notation (base 8). The 'base' a number is written in is simply the number that shows as '10' when you write it down. For example, in binary notation (base 2), the number written '10' would be 2, the number written '100' would be 4, the number written '1000' would be 8, etc. Similarly, the number written '11010' would be 26, because it has one 16, one 8, zero 4s, one 2 and zero 1s, and 16+8+2=26. In trinary (base 3), 38 would be written '1102', because it has one 27, one 9, zero 3s and two 1s. And in base 10, which is what we usually use for writing numbers, 156 equals 156 because it has one 100, five 10s and six 1s. So, based on the same principle, if you take 31 in base 8 and transpose it into base 10, you have three 8s and one 1, 3*8=24, 24+1=25, so 31 in octal is 25 in decimal.