### Algebraic K-theory via binary complexes, by Daniel R. Grayson

[ 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 K_{1}, we introduce binary complexes
and use them to provide generators and relations for all the algebraic K-groups
of an arbitrary exact category.

Daniel R. Grayson <drg@illinois.edu>