When Satoshi decided to use 21 million Bitcoins (BTC) as the finite number of Bitcoins, the global M1 money supply approximately stood at $21 Trillion USD. Every dollar can be divided into 100 cents, making the total number of the pieces of money to exist at around 2100 trillion. Why this number so crucial is a question many investors ask and the importance of having 21 million BTC pieces as the maximum cap.
Bitcoin’s whitepaper offers three crucial phrases that point out the calculation of the ‘mysterious’ 21 million figure.
Given these parameters and a 10 minute average time to mine a block, the total will be 21 million as shown in the equations below.
Factoring out common terms (50*210,000) we get the following equation.
The later part of the equation adds up to 2 (or very close to 2) tending to infinity. This collapses the equation to;
First, M1 money represents the most liquid type of money available and it facilitates easy payments across the world. Bitcoin on its part was created to allow worldwide transactions and become the global currency, basically replacing all fiat currencies. As explained above, the total pieces of money in 2008 translated to roughly 2100 trillion pieces. This was a key figure in determining the number of Bitcoin pieces.
The total number of Bitcoins to ever be mined stands at 21 million, which infers that the total Bitcoin pieces ever to exist will stand at 2100 trillion (a similar number to M1 supply), as one Bitcoin can be divided into eight parts. This figure rightly fits to Bitcoin replacing the M1 supply of money in future once all coins are mined (presumably in 2140) without a deficiency.
(This section is from the original Medium article)
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.