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Consider the following Moore’s law growth pattern (since 1980) for the number of transistors inside a particular commercial microprocessor: N = 1920 x 10 0.1637(Y – 1980) where Y is the year and N is the number of transistors. Assuming sustained Moore’s law growth, what will be the number of transistors in a microprocessor in year 2025? Using the same expression, calculate how many years it will take for the transistor count to increase by 100x

Respuesta :

Answer:

No. of transistors = [tex]$4.1524 \times 10^{10}$[/tex] transistors

Explanation:

Given that:

N = [tex]$1920 \times 10^{0.163(Y-1980)}$[/tex]

Y = 2025

N = [tex]$1920 \times 10^{0.163(2025-1980)}$[/tex]

N = [tex]$4.1524 \times 10^{10}$[/tex] transistors

Now at Y = 1980

Number of transistors N = 1920

Therefore,

[tex]$1000 = 10^{0.163(Y-1980)}$[/tex]

[tex]$\log_{10} 1000=0.163(Y-1980)$[/tex]

[tex]$\frac{3}{0.163}=Y-1980$[/tex]

18 ≅ 18.4 = Y - 1980

Y = 1980 + 18

   = 1998

So, to increase multiples of 1000 transistors. it takes 18 years.

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