An low power vector summation apparatus is provided for using 2's complement arithmetic without the high switching activity of the prior art. In particular, the invention operates to exploit the sign-extension property of a 2's complement number. A reduced representation for 2's complement numbers is provided to avoid sign-extension and the switching of sign-extension bits. The maximum magnitude of a 2's complement number is detected and its reduced representation is dynamically generated to represent the signal. A constant error introduced by the reduced representation is also dynamically compensated.