An algorithm to convert redundant number representations into conventional representations is presented. The algorithm is performed concurrently with the digit-by-digit generation of redundant forms by schemes such as SRT division. It has a step delay roughly equivalent to the delay of a carry-save adder and simple implementation. The conversion scheme is applicable in arithmetic algorithms such as nonrestoring division, square root, and on-line operations in which redundantly represented results are generated in a digit-by-digit manner, from most significant to least significant.

On-the-Fly Conversion of Redundant into Conventional Representations

In this correspondence we analyze the computational complexity of fault detection problems for combinational circuits and propose an approach to design for testability. Although major fault detection problems have been known to be in general NP-complete, they were proven for rather complex circuits. In this correspondence we show that these are still NP-complete even for monotone circuits, and thus for unate circuits. We show that for k-level (k ≥ 3) monotone/unate circuits these problems are still NP-complete, but that these are solvable in polynomial time for 2-level monotone/unate circuits. A class of circuits for which these fault detection problems are solvable in polynomial time is presented. Ripple-carry adders, decoder circuits, linear circuits, etc., belong to this class. A design approach is also presented in which an arbitrary given circuit is changed to such an easily testable circuit by inserting a few additional test-points.

The Complexity of Fault Detection Problems for Combinational Logic Circuits

A data compression technique called self-testable and error-propagating space compression is proposed and analyzed. Faults in a realization of Exclusive-OR and Exclusive-NOR gates are analyzed, and the use of these gates in the design of self-testing and error propagating space compressors is discussed. It is argued that the proposed data-compression technique reduce the hardware complexity in built-in self-test (BIST) logic designs using external tester environments. >

A data compression technique for built-in self-test

Presentation et analyse d'une technique de compression, appelee compression spaciale, applicable a la compression de donnees de tests soit dans l'environnement BIST soit dans l'environnement externe

Conventional schemes for fast multiplication accumulate the partial products in redundant form (carry-save or signed-digit) and convert the result to conventional representation in the last step. This step requires a carry-propagate adder which is comparatively slow and occupies a significant area of the chip in a VLSI implementation. A report is presented on a multiplication scheme (left-to-right, carry-free, LRCF) that does not require this carry-propagate step. The LRCF scheme performs the multiplication most-significant bit first and produces a conventional sign-and-magnitude product (most significant n bits) by means of an on-the-fly conversion. The resulting implementation is fast and regular and is very well suited for VLSI. The LRCF scheme for general radix r and a radix-4 signed-digit implementation are presented. >

Fast multiplication without carry-propagate addition

The problem of fault detection and location in tree networks of two input EXCLUSIVE-OR (EOR) gates is considered. The fault model assumes that an EOR gate can change to any other function of its two inputs except the equivalence function. An efficient procedure for single fault location is presented. In the worst case the number of tests necessary to locate single faults is bounded by a linear function of the number of input variables. Constructive upper bounds are obtained for the number of tests to detect multiple faults. Optimality of these bounds is argued and extension of results to other types of networks is considered.

https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1031&context=csearticles

K. L. Kodandapani

Papers

Diagnosis of Faults in Linear Tree Networks