Because of Moore's Law, the ________ of data processing is approaching zero.

Question

BlackTom AI · Accepted Answer

Moore’s Law states that transistor density on integrated circuits roughly doubles every 18–24 months, so the cost per transistor (and thus per unit of data processing) falls rapidly over time. This leads directly to the conclusion that the cost of data processing is approaching zero.

1. Relevant knowledge points and concepts
- Moore’s Law: exponential growth in transistor count on a chip over time.
- Cost-per-function: as more transistors are available for the same manufacturing cost, the cost to perform a given unit of computation decreases.
- Asymptotic behavior of exponential decay: repeated halvings lead toward zero.

2. Step-by-step reasoning
- If transistor count doubles each period while manufacturing and packaging costs remain similar, then the cost per transistor is approximately halved each period.
- Let C0 be the initial cost per computing unit. After n doubling periods, cost Cn ≈ C0 · (1/2)^n.
- As n increases without bound, (1/2)^n → 0, so Cn → 0. Therefore cost per unit of processing approaches zero.

3. Calculation (intermediate steps)
- Cn = C0 · (1/2)^n.
- Example: after 3 doubling periods, C3 = C0 · (1/2)^3 = C0 · 1/8.
- Limit: lim_{n→∞} C0 · (1/2)^n = C0 · 0 = 0.

4. Why the correct answer is correct
- The phrase “Because of Moore’s Law” refers to exponential increases in transistor density and corresponding reductions in cost per transistor/function. Thus “cost” is the quantity that is driven toward zero by Moore’s Law.

5. Why other options are incorrect
- Use: Moore’s Law increases availability and tends to increase use, not reduce it to zero.
- Power: energy per operation has decreased, but total power consumption can rise with more devices; it does not asymptotically approach zero in the same clear theoretical way.
- Applications: number of applications grows with capability, not goes to zero.
- Speed: transistor switching speeds improved historically but do not approach zero (that would mean infinitely slow); they increase, not decline to zero.

6. Conclusion
Given the exponential fall in cost-per-computation implied by Moore’s Law, the correct answer is “cost,” which matches the provided answer.

Because of Moore's Law, the ________ of data processing is approaching zero.单项选择题

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