# Analysis of the Provided Image The image contains questions related to detecting faults in digital logic circuits, specifically AND-OR and OR-AND circuits. The questions ask for test sets for given Boolean logic expressions. --- ## **4. AND-OR Circuits** Given functions: - **f1(A, B, C, D) = B'D' + AC + BC'D** - **f2(A, B, C, D) = A'B + BD + ACD** The task is to find tests to detect faults for these circuits. --- ## **5. OR-AND Circuits** Given functions: - **g1(A, B, C, D) = (A + D')(B' + C)(A' + C' + D)** - **g2(A, B, C, D) = (A + C)(A + D)(B' + C + D)** *(handwritten)* The task is the same: find tests to detect faults. --- ### **Test Set Explanation (General Guidance)** To find tests to detect faults for these circuits, typically you want to: - Find input combinations (test vectors) that will activate and propagate possible faults (like stuck-at- or stuck-at-1) at each gate to the output. - You do this by analyzing the circuit's Boolean expressions and considering each gate's output. ### **For Example** #### **For f1(A, B, C, D):** - Consider each term as an OR gate input: - *B'D'* (AND gate) - *AC* (AND gate) - *BC'D* (AND gate) - You would create test vectors where each AND gate is uniquely activated (i.e., its output is 1, others are ), and see if the output matches expectation. #### **For g1(A, B, C, D):** - This is an OR-AND circuit, so each parenthesis is an OR gate, and the overall output is the AND. - Test vectors would be chosen to test each OR gate's output individually. --- ## **Conclusion** - The image contains Boolean functions for which test vectors to detect faults need to be found. - The handwritten part provides the expression for **g2(A, B, C, D)** but does not provide the test vectors themselves. --- If you'd like, I can help find the test vectors for any of these functions. Please specify which one you'd like to start with!