**64 ain’t enough**

It seems a great deal to have **64 bits** to address memory.

Take the integer value of 2^{64} = 18446744073709551616: that’s more than **18 followed by 18 zeros**, or 18 exa (mega, M = 10^{6}; giga, G = 10^{9}; tera, T = 10^{12}; peta, P, 10^{15}; exa, E, 10^{18}).

One can say that if your 32-bit address space were a the volume of a **drop of water** (1 mm^{3}), then the 64-bit address space is a **sphere of 5.7 km diameter**.

The number 2^{64} is also related to that legend on the creation of the game of chess where the inventor asked as reward the number of **grains of wheat** that you can count on a **chessboard** if one grain were placed on the first square, two on the second, four on the third and so on, doubling the number of grains on each subsequent square. It turns out that the resulting amount of wheat is larger than a thousand years of today’s world production !

Or, you just need 44 bits to address each dollar in the current U.S. National Debt: **13.9 10 ^{12}** $ (about 14 teradollars); and it will take some time to use all the bits, since the current trend is doubling (i.e. one additional bit) every 8 years, so 64 bits should be enough for

**160 years**.

But if you try to address every single **molecule** in a drop of water (1 mm^{3} = 1 g = 1/18 mol so 1/18^{th} of the Avogadro constant N_{A} or 3.34 10^{22}) then you’ll see that you are missing a few bits ! Actually to represent **N _{A} = 6,022141793 10^{23} 1/mol** = 602 zetta/mol (zetta, Z, 10

^{21}) as an integer, you’ll need

**75 bits**. Quite remarkably, 2

^{75}is very close to N

_{A}: 2

^{75}/ N

_{A}= 1.003.

So we can say that computer science and finance still haven’t catched up with chemistry.