Abstract—The Boolean difference is defined. It is shown through example how the Boolean difference is used to analyze the effect of errors on the outputs of logic circuits. Examples are given of error detection problems, analysis of redundant logic, and the generation of diagnostic sequences.

The correct operation of addition in a digital computer is very important. In this paper, the authors exhibit a checking scheme called ``carry-dependent sum add'' which is based on the parity prediction method. This scheme assures single-fault detection without duplication of the carry circuit. An example of a binary adder and a decimal adder using this scheme are included.

A block code is presented that will correct an error consisting of the gain or loss of a bit (binary digit) within the block. The code can be generalized to correct the loss or gain of a burst of bits. A further feature is the possibility of correcting additive errors appearing in the vicinity of the bit loss or gain. An additive error is a bit changed from 0 to 1 or from 1 to 0. The code is constructed by inserting a known character into a burst-error-correcting code at periodic intervals. The known character locates the approximate position of the bit loss or gain. At the location a bit is inserted or removed from the block, depending on whether a loss or a gain has occurred. The error-correcting code then corrects the erroneous bits between where the error occurred and where the correction took place.