The solution to a homework problem found that the number of mantissa bits used t

Question

The solution to a homework problem found that the number of mantissa bits used to express a floating point or real number in an Excel spreadsheet is 50. You are using an Excel spreadsheet to count molecules by successively adding 1 to the previous cell. Assuming that there is no limit to the number of rows and columns in a spreadsheet, and starting from zero, how many bits would be necessary to accurately count to Avagadro's number (6.02252 Times 10^23) of molecules. Show calculations to justify your results.

Explanation / Answer

Number of bits required to represent any number n is equal to ceiling(log2(n) + 1)

So, to represent Avogadro’s number we need ceiling(log2(6.02252*10^23) + 1) = 80

* ceiling(x) is the smallest integer not less than x. E.g ceiling(2.1) = 3, ceiling(4.9) = 5

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