A quaternary complex number CCD adder (abstract only)

Abstract

Complex number arithmetic occurs frequently in digital signal processing and power systems analysis. Normally, complex numbers are given two binary words, with one word for each component (real and imaginary). Therefore, the standard binary implementation of complex numbers requires several real arithmetic operations. Besides, the two components of each complex number must be tracked down at every stage of the computation. Different digital representations for complex numbers have been proposed in an effort to reduce these problems. Knuth [1] has proposed an unconventional single component representation of complex numbers whereby the radix is chosen to be (2j) with the digit set comprised of the first four positive integers (0, 1, 2, 3). This is in contrast with the conventional two components representation with binary radix whether in Cartesian or Polar coordinates. Knuth's representation leads to simple and interesting arithmetic in the complex field [2] [3].In this paper, the realization of a quaternary (4-valued) complex number adder using charge coupled devices (CCD's) is presented. The adder is based on Knuth's complex number system. The design employees multi-valued CCD gates (inhibit, fixed-overflow, addition, constant) [4]. These gates constitute a functionally complete set of operators in the charge domain i.e. any function can be represented using only these four gates. In addition, CCD technology has the inherent advantages of low power consumption, high packing density and MOS compatibility, which make it suitable for VLSI implementation. On the other hand, the low speed problem of CCD's remains to be solved.Any complex number is representable in Knuth's system as follows: X =