## 4 Evaluation
### Results Analysis
#### 4.3.4 Section 4: Analysis  
This section's assessment comprised 23 questions focused on arithmetic and logical operations in _Verilog_, including addition, subtraction, multiplication, division, and modulus, with both unsigned and signed number representations. Additional topics covered shift operations, relational comparisons, and bit-wise and logical operations. Due to the broad range of _Verilog_ operations addressed, the assessment was more extensive and complex compared to previous sections. Group 1 Test Results  
As shown in Figure 20, most questions did not achieve an average accuracy upon first submission above 90%. This is primarily because the arithmetic operations in _Verilog_ involve numerous underlying concepts; simply memorizing procedures is insufficient, and a deeper, integrated understanding is required to achieve higher accuracy. While repeated practice enabled the final accuracy rates to approach 100%, some items still fell short of complete mastery. The following provides a more detailed analysis of these questions. From the overall assessment results, the reasons for certain questions obtaining notably lower average accuracy upon first submission are as follows:  
* Question 4: This topic focused on how division is performed in binary, which differs somewhat from traditional decimal division. This unfamiliarity resulted in a lower initial accuracy. However, after students understood the underlying computational method, the final accuracy rose to 99%, indicating that although the problem was challenging, students were able to master the concept through guided practice. * Question 6: This question addressed signed binary addition, which requires students to account for sign extension and overflow conditions not present in unsigned addition. The need for additional reasoning resulted in a lower first-attempt accuracy. Nevertheless, after multiple attempts and conceptual clarification, students' final accuracy reared 100%. * Question 8: Students performed signed multiplication--a more complex process requiring a comprehensive understanding of the binary arithmetic rules. As expected, both the average number of attempts and initial accuracy were less favorable; the final accuracy for this item was 95.3%. This may be attributed to the complexity of the problem, insufficiently detailed guidance, or gaps in the design of the problem, suggesting areas for improvement. Figure 19: Individual student performance for Group 2 in Section 3. * Question 12: This question involved binary signal concatenation and replication. The first-attempt accuracy was only 48.6%, which is relatively low. Upon review, the item itself did not appear excessively complex. The lower accuracy may have resulted from unclear wording in the question, leading to overlooked details, or from the abstract nature of the concept for beginners. * Questions 8, 10, 11, and 12: These questions had the lowest final accuracy rates, all below 98%. These topics primarily concerned signed operations, which students found more challenging, as expected given their increased complexity. To address this, future improvements could include breaking down complex concepts into more granular subtopics for smoother learning curves, or increasing the number of practice problems to reinforce understanding through repetition. Individual Student Performance in Group 1  
Figure 21 displays the performance of individual Group 1 students in Section 4. Several key observations can be made:  
1. Increased Number of Submissions Indicates Greater Learning Challenges: The chart shows that most students required more submissions per question than in previous sections. For the students beyond ID 24, the average number of submissions commonly exceeded two, with those in the latter part of the group needing four to six attempts or more. This reflects the heightened difficulty of this section, which covers a wide range of complex arithmetic and logic operations, necessitating repeated practice to arrive at correct solutions. 2.