Concurrent Error Detection for Group Look-ahead Binary Adders

TLDR

Group look‑ahead adders rely on Boolean statements and Boolean‑difference analysis to assess coverage of error‑checking schemes. The study evaluates the relative merits of residue‑mod‑3 and parity‑prediction concurrent error‑detection schemes for group look‑ahead adders. The authors compare the two schemes by tabulating circuit element counts and applying Boolean‑difference coverage calculations. Residue‑mod‑3 checking is only economical when operands already carry mod‑3 bits, whereas parity‑prediction checking offers a cost advantage in systems with three or more data‑transfer checks, highlighting weaknesses in earlier coverage analyses.

Abstract

This paper presents an evaluation of the relative merits of two schemes for performing concurrent error detection in group look-ahead adders. One of the schemes is a residue mod 3 check and the other is a parity prediction check. The Boolean statements that define the operation of group look-ahead adders, concurrent error detection and the Boolean difference serve as background for interpreting the results of the study. The Boolean difference is a tool for calculating the “coverage” of elements in a logical network by error-checking schemes. Some weaknesses in prior studies of coverage calculation are brought to light. Tables showing the number of circuit elements in the various portions of adder and error-checking circuits are given. It is shown that the residue mod 3 check adder is not economical unless the addition operands are already provided with the mod 3 check bits. Thus, a worthwhile comparison of the checking schemes should not proceed without considering the overall data flow checking strategy. In machine organizations with three or more data transfer checks, the parity-checked adder seems to offer a cost advantage.