[ May 19, 2012: replaced the previous version by the final version, which will
appear in the Journal of the American Mathematical Society. ]
[ Jun 14, 2011: replaced the previous version to include some details of some proofs and
to add a bit to the introduction. ]
[ Apr 15, 2011: replaced the previous version to expand a definition, fix a reference,
and to add a bit to the introduction. ]
[ Jan 22, 2011: replaced the version dated Jan 6, 2011, to fix a reference. ]
Motivated by work of Nenashev on K1, we introduce binary complexes
and use them to provide generators and relations for all the algebraic K-groups
of an arbitrary exact category.