Analog techniques for residue operations

The precision required for residue operations is primarily associated with resistive components and operational amplifiers. However, technology has advanced to the point that analog components can be built to an accuracy of less than one tenth of one percent (at least with discrete components). Companies are attempting to build DAC'S with fifteen (15) bit accuracy which will settle to the least significant bit in one hundred (100) nanoseconds. None are commercially available but seven or eight bit DAC's with settling times on the order of one hundred (100) nanoseconds are not uncommon. Sixteen (16) bit ADC's have been announced recently as a result of new analog components. It is not uncommon to find operational amplifiers on the market with gain bandwidth products in excess of one hundred fifty (150) megahertz and linearities on the order of one tenth of one percent. One can also find analog voltage comparators (such as the Motorola MC1650) which has a hysteresis of ten millivolts and a switching speed of less than two nanoseconds. Shotkey diodes have been introduced which allow transistors to switch in less than one and one-half nanoseconds, and manufacturers have learned to build both active and passive components to a tolerance of less than one-tenth of one percent.