The maximum number of bitcoins that will ever be in circulation is 21 million. Since each bitcoin can be divided into 100 million parts, the maximum number of bitcoin pieces that will ever be in circulation is 2100 trillion. Two reasons this choice was a great idea involve floating point arithmetic and the global money supply.

Floating Point Arithmetic

Floating point arithmetic is a type of mathematics used by computers to handle decimals. Decimals are often represented with 64 bits where one bit denotes the sign, 11 bits denote an exponent, and, 52 bits denote a fraction. To avoid rounding errors, it is often a good idea to avoid integers that cannot be represented with only the fraction bits. To be extra safe, it may help to also leave one fraction bit unused. With respect to 64 bit decimals, that would limit integers to 51 bits. The maximum integer that can represented with 51 bits is just slightly over 2100 trillion!

Global Money Supply

A safe choice for a cryptocurrency is to make sure it can potentially replace all the money in the world. There are many ways to estimate the global money supply. One estimate that includes the most liquid types of money is referred to as M1. Around the time bitcoin was designed, the global M1 money supply was approximately $21 trillion. Since dollars can be divided into at most 100 cents, the most pieces that global money supply can ever be divided into is 2100 trillion!

Conclusion

Although the maximum number of bitcoin pieces seems arbitrary, there are sound reasons for the selection. It helps avoid errors on most computer systems, and, is likely sufficient for all possible transactions everywhere.

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Acknowledgements

I would like to thank IOHK (Input Output Hong Kong) for funding this effort.

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