Logic Operators on Delta-Sigma Bit-Streams

Abstract: The fundamental logic operations NOT, OR, AND, and XOR processing bit-streams of ∆Σ-modulators are discussed herein. The resulting bit-streams are evaluated on the basis of their mean values and their standard deviations. Mathematical expressions are presented for their mean values; i.e., the logic function XOR results in the negative multiplication of two bipolar bit-streams, and the logic function AND results in the multiplication of two unipolar bit-streams. As the results are valid for bit-streams with independent high-frequency components, the normed cross-product is utilized for evaluation of the independence of the high-frequency components. In order to achieve a high independence between the input bit-streams, representing the same value, the quantization noise is affected. Multiple strategies are examined and ∆Σ-modulators with different designs are chosen as the best-suited solution. The operations are evaluated on a testbench.