[Groop] Re: I'm sure we have done this before, but ...

[E C]

Hi guys/grrls!

A decimal system has ten numbers (0, 1, 2, 3, 4, 5,
6, 7, 8, and 9).

A binary system has two numbers (0 and 1).

A decimal system is based on the number 10.  For
example:

     1234 = 1x1000 + 2x100 + 3x10 + 4x1
     where 1000 is 10 to the 3rd power (10x10x10)
           100  is 10 to the 2nd power (10x10)
           10   is 10 to the 1st power (10)
           1    is 10 to the 0th power (1)
 
A binary system is based on the number 2.  For
example:

     1010 in binary = 1x8 + 0x4 + 1x2 + 0x1 in decimal
     where 8 is 2 to the 3rd power (2x2x2)
           4 is 2 to the 2nd power (2x2)
           2 is 2 to the 1st power (2)
           1 is 2 to the 0th power (1)

     0111 in binary = 0x8 + 1x4 + 1x2 + 1x1 in decimal

There is also binary logic (used in digital logic in
computers).  It's sometimes called Boolean logic, named
after George Boole.

A "+" means logical "OR".

     0 + 0 = (0 or 0) = 0
     0 + 1 = (0 or 1) = 1
     1 + 0 = (1 or 0) = 1
     1 + 1 = (1 or 1) = 1

A "." means logical "AND".

     0 . 0 = (0 and 0) = 0
     0 . 1 = (0 and 1) = 0
     1 . 0 = (1 and 0) = 0
     1 . 1 = (1 and 1) = 1

You can also use "1" and "0" to mean "true" or
"false".  "1" means "true".  "0" means "false".

Sooo,

     "There are only 10 types of programmers,
     those who know binary and those who don't."

In this sentence "10" doesn't mean "ten".  It's
supposed to mean a "1" and a "0" (binary).  It
also references "true" and "false".  Either
"you know binary" (similar to a "true") or
"you don't know binary" (similar to a "false").

See you.

Eric


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