1. An arithmetic unit suitable for large scale integration for computing summed indexed products comprising: 1. a vector adder for bit serial, word serial binary data containing sign and magnitude information, comprising: a. a first sign changing means to which serial binary data is applied from a first data input terminal (d.sub.1) and subject to a first sign control input (c.sub.1), b. a first serial summer to which two serial binary data streams are applied respectively from the output of said first sign changing means and from a second data input terminal (d.sub.2), said summer producing a first output quantity (s.sub.1) where EQU s.sub.1 = (d.sub.2 .+-. d.sub.1) c. a second sign changing means to which serial binary data is applied from said first summer and subject to a second sign control input (c.sub.2), d. a second serial summer to which two serial binary data streams are applied respectively from the output of said second sign changing means and from the output of a third data input terminal (d.sub.3), said summer producing a second output quantity (s.sub.2), where EQU s.sub.2 = [d.sub.3 .+-. (d.sub.2 .+-. d.sub.1)] 2.