Part a: The number of transistors per IC in 1972 seems to be about 4,000 (a rough estimate by eye). Using this estimate and Moore's Law, what would you predict the number of transistors per IC to be 20 years later, in 1992 ? Prediction = Number Part b: From the chart, estimate (roughly) the number of transistors per IC in 2014. Using your estimate and Moore's Law, what would you predict the number of transistors per IC to be in 2040? Part c: Do you think that your 2040 prediction in Part b is technologically achievable? Why or why not?

Let's address each part of your question step by step. --- ### **Part a** **Prediction of Transistors per IC in 1992 Using Moore's Law** - **Starting Point (1972):** 4,000 transistors per IC. - **Time Span:** 20 years (from 1972 to 1992). - **Moore's Law:** Number of transistors doubles approximately every 2 years. **Calculations:** 1. **Number of Doublings:** \[ \text{Number of Doublings} = \frac{20 \text{ years}}{2 \text{ years/doubling}} = 10 \text{ doublings} \] 2. **Predicted Number of Transistors in 1992:** \[ \text{Transistors} = 4{,}000 \times 2^{10} = 4{,}000 \times 1{,}024 = 4{,}096{,}000 \] **Prediction:** \[ \boxed{4{,}096{,}000 \text{ transistors per IC in 1992}} \] --- ### **Part b** **Estimating Transistors per IC in 2014 and Predicting for 2040** 1. **Estimating Transistors in 2014:** Assuming the trend continued: - **Time Span from 1992 to 2014:** 22 years. - **Number of Doublings:** \( \frac{22}{2} = 11 \) doublings. \[ \text{Transistors in 2014} = 4{,}096{,}000 \times 2^{11} = 4{,}096{,}000 \times 2{,}048 = 8{,}388{,}608{,}000 \approx 8{,}388{,}608{,}000 \text{ transistors} \] **Estimated Transistors in 2014:** Approximately **8.4 billion** transistors per IC. 2. **Predicting Transistors in 2040:** - **Time Span from 2014 to 2040:** 26 years. - **Number of Doublings:** \( \frac{26}{2} = 13 \) doublings. \[ \text{Transistors in 2040} = 8{,}388{,}608{,}000 \times 2^{13} = 8{,}388{,}608{,}000 \times 8{,}192 \approx 68{,}719{,}476{,}736{,}000 \text{ transistors} \] **Predicted Transistors in 2040:** Approximately **68.7 trillion** transistors per IC. **Summary:** - **2014 Estimate:** ~8.4 billion transistors per IC. - **2040 Prediction:** ~68.7 trillion transistors per IC. --- ### **Part c** **Assessment of the Technological Feasibility for 2040 Prediction** While Moore's Law has been remarkably accurate for several decades, predicting a transistor count of approximately **68.7 trillion transistors per IC by 2040** poses significant technological challenges: 1. **Physical Limitations:** - **Atomic Scale Constraints:** Transistors are approaching sizes where quantum effects become significant, making further miniaturization difficult. 2. **Heat Dissipation:** - **Thermal Management:** More transistors generate more heat, which can affect performance and reliability. Efficient cooling solutions would be essential. 3. **Manufacturing Challenges:** - **Photolithography Limits:** Current manufacturing techniques may struggle to create such densely packed transistors without defects. 4. **Economic Factors:** - **Cost Efficiency:** The cost of producing ICs with trillions of transistors would need to be economically viable for widespread adoption. 5. **Alternative Technologies:** - **Emerging Paradigms:** Quantum computing, neuromorphic chips, or other innovative architectures might replace traditional transistor-based ICs, altering the trajectory implied by Moore's Law. **Conclusion:** Given these substantial hurdles, achieving **68.7 trillion transistors per IC by 2040** appears **untenable with current technological trends**. It is likely that alternative approaches to computing and chip design will emerge, potentially redefining or superseding Moore's Law in the process.