Counting from 1 to an Integer… in Binary
APL, 10 characters

Another on in APL. Assumes⎕IO←1 (the default). No bonus points. Reads the number from the input device. If your APL uses 64 bit integers instead of 32 bit integers, substitute 64 for 32 as needed.

Notice that APL transparently converts to floating point numbers when the range of an integer is exceeded. It's hard thus to exactly say what integer size APL works with.

⍉(32⍴2)⊤⍳⎕


explanation

2          ⍝ the number 2
32⍴2       ⍝ a vector of 32 twos.
(32⍴2)⊤X   ⍝ X represented as base 2 to 32 digits precision
⍳X         ⍝ a vector of the integers from 1 to X
⎕          ⍝ a number queried from the terminal
(32⍴2)⊤⍳⎕  ⍝ the output we want, flipped by 90°
⍉(32⍴2)⊤⍳⎕ ⍝ the output we want in correct orientation (⍉ is transpose)