Exponential Examples

Last updated: 2012 May 23

If you print a number 2GB (2³¹ Bytes) long in binary, which consists of 2147483647 bits using a 9 pt font, each character takes 1/8 of an inch, hence the number of bytes is also a good approximation for the number of inches of the printed maximum number:

In feet: 178956971 (=2147483647/12)
In miles: 33893 (=17895697/5280)
Which would wrap around the earth about one and a half times (circumference of the Earth is about 21000 miles)!

To type 1GB (2³⁰ Bytes) at 100 characters per minute, would take about 216705.7 hours (1024*1024*1024/100*60).
At 40 hours per week this is just over 104 years (216705.7/(40*52)).

Assume it takes 0.01 seconds to try a key to crack an encrypted file with a 1000 byte key by brute force, given that every possible key had to be tried.

This would take about (0.01*(2^8*1000)) seconds. Since 2¹⁰ is about 10³, the above time is about 10²³⁹⁸ seconds.

There are 3600(seconds/hour)*24(hours/day)*365(days/year) = 31,536,000 seconds per year.

So this would take over 3*10²³⁹¹ years. The age of the universe is about 1.375*10¹⁰ years.
That is, it would take a time which is a billion times a billion (about 264 times a billion) the age of the universe!

If the key is 10KB then the time is exponentially larger (calculation left as an exercise).