The e-derivative Boolean differential equation and logic circuit detection

Using the derivative of Boolean functions and the e-derivative defined by ourselves as research tools, we study the problem of derivative differential equation error detection and e-derivative differential equation error detection for logic circuits. The following conclusions are drawn: the 0-error (or 1-error) of a logic line in some logic circuits can be detected by the derivative Boolean differential equation but not by the e-derivative Boolean differential equation; the 0-error (or 1-error) of a logic line in some logic circuits can be detected by the e-derivative differential equation but not by the derivative Boolean differential equation; the 0-error and 1-error of some logic circuits can be detected by both derivative and e-derivative Boolean differential equation. It shows that, the error detection of e-derivative is an indispensable logic circuit detection method.