The rapid pace of hardware development in DSP tends to render any material obsolete before the printer’s ink dries. We have thus attempted to present hardware concepts that are fundamental and invariant under any future changes. Boolean algebra, switching circuits, and memory elements provide the basis for all digital mechanizations, whether they be dedicated processors, programmable processors, or networks of processors. An input design principle is the desirability to maintain appropriate balance among arithmetic speed, data movement, and system control.

The expression that characterizes many of the important signal processing algorithms is the sum of products. Multiplication is the pervading arithmetic operation and is covered by a discussion of both parallel (array) and serial multiplier circuits. Microprogramming, whether user accessible or embedded in the hardware, provides efficient control of the arithmetic functions.

An alternative to the hardware multiplier is the memory-based distributed arithmetic direct realization of the sum of products. The simplicity and regularity of this structure makes it attractive for VLSI implementation.