Use of switching circuits as redundant multiplier elements in canonic digital networks

Switching circuits are used to realize elementary multipliers whose coefficients are restricted to integer powers of 2. Modifications are given to accommodate signed magnitude, 1´s complement and 2´s complement binary codes. The addition of a single elementary multiplier to a canonic digital network and its interchange with each conventional multiplier in turn enables the multiplier coefficients to be respecified with a corresponding change in gain (which need never exceed ¿2). The errors in the multiplier coefficient approximations may then be evaluated for the different sets of coefficients, and the most suitable set selected. A simple analysis procedure is given with an error criterion which provides a suitable assessment of the quantization errors resulting from multiplications. With fixed-point arithmetic, elementary multipliers provide scaling for conventional multipliers to enable the most significant bit in the coefficients to be used.