I am trying to understand the underlying concept of Bitcoins and could only find the PDF here:
http://sourceforge.net/projects/bitcoin/files/Design%20Paper/bitcoin.pdf/bitcoin.pdf/download
(and Wikipedia)
They detail the system in very general terms. What I don't understand in the money creation: A coin is a chain of transactions. So a „freshly minted“ coin is a coin that only contains a Nonce that Hashes to the goal, which is a Number smaller than a given $target. Where is the incentive for the user to Hash the Block? As I understand it, the incentive basically lies in: „If I calculate the Hash and it Hashes to a Number smaller $target, then I found a new coin“. But if the user wants to create coins, wouldn't it be more efficient to skip the Hashing and concentrate on Number crunching?
„By convention, the first transaction in a block is a special transaction that starts a new coin owned by the creator of the block.“
But by broadcasting this proof of work, anybody could claim the coin because the old Hash + Nonce = new Hash have to be available for the check of the proof of work?

A second question: How are coins subdivided? I thought a coin starts with a certain Nonce and is the smallest unit but gavinandresen
http://bitcointalk.org/index.php?topic=198.0
says a coin can be subdivided again.

Is there an example how bitcoin works on a bit-level?

Richard