Combinational arithmetic systems for the approximation

The concepts of arithmetic building blocks (ABB) and combinational arithmetic (CA) nets as well as their applications have been previously reported in References 3, 4, and 5. The unique ABB, resulting from the efforts of minimizing the set of building blocks in Reference 3, is designed at the arithmetic level, employing the redundant signed-digit number system,2 and is to be implemented as one package by LSI techniques. The ABB performs arithmetic operations on individual digits of radix r > 2 and its main transfer functions are: the sum (symbol +) and product (symbol *) of two digits, the multiple sum of m digits (m ::; r + 1), (symbol ¢), and the reconversion to a non-redundant form (symbol RS). A single ABB may serve as the arithmetic processor of a serially organized computer. Many ABB's can be interconnected to form parallel arrays called combinational arithmetic (CA) nets which compute sums, products, quotients, or evaluate more complex functions: trigonometric, exponential, logarithmic, gamma, etc. Because of the use of signed-digit numbers, the parallel addition and multiplication speed is independent of the length of operands. A design procedure has been developed for CA netsS-a given algorithm is initially represented by a directed graph (algorithm graph, or A-graph), which is then converted to an interconnected diagram of ABB's (hardware graph, or H-graph). The delay through one ABB is defined to be one time unit,