Quickly estimate 2^64 without using a pen/papar.

Question

Saurabh · Accepted Answer

2 ^ 10 = 1.024 * (10^3)
2 ^ 60 = (1.024 ^ 6) * (10 ^ 18)
2 ^ 64 = (16 *  (1.024 ^ 6) * (10 ^ 18) )
All, we need to solve is 1.024 ^ 6. using binomial expansion, ignoring the smaller terms we get  : (1 + 0.024) ^ 6 = 1 + 6 * 0.024 = 1.144 = 1.15 (approx)
Hence the answer is : (16 * 1.15) * (10 ^ 18) = 18.4 * (10 ^ 18)

It is much closer to the actual answer and very fast to calculate.

Kaustubh · Answer

2^10=1024 ~10^3
2^64=(2^10)^6 * 2^4
=> (10^3)^6*16
=> 10^18*16
=> 1.6 * 10 ^ 19

= 16,000,000,000,000,000,000

Calculator says: 18,446,744,073,709,551,616

m · Answer

2^32 ~= 4 bil
2^64 = 4bil * 4 bil
= 16 bil bil
each bil 9 0's, so 16 with 18 0's.

Anon · Answer

well in binary, 1 followed by 64 0s.

They didn't specify answer should be in decimal.

Vivek · Answer

It is 16 billion billions

justaguye · Answer

Well, 2^8 is 256 and 2^16 is that squared, which should have 5 digits..
If I square it again, I should have double those digits, and again if I square it again..
So I'm looking for something in the neighborhood of 1x10^20, or approx
10,000,000,000,000,000,000.
Calculator says: 18,446,744,073,709,551,616--> I'm in the ballpark.

bt · Answer

Donno if this is to test witt and prepness.. 
I would say 18,446,.... so on
He ll ask how i get that..
Say "calculator"
The question was about without using pen/paper

patanjal.vyas@gmail.com · Answer

They are talking about 64 bit integer, where left most bit is set to 1, and rest to 0. Considering it is 64 bit unsigned integer, it should be equal to value of 32 unsigned integer where all bits are 1, which I guess is somewhere around 4billion, or you can just say 2^64 = UInt32.MaxValue

fasahat khan from karachi pakistan B-64 blk 4-A Gulshan e iqbal karachi journalist society 75300 · Answer

2^64 the answer is 32

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