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Recently at TigerBeetle, we’ve decided to use 128-bit integers to store all financial amounts and balances, retiring our previous use of 64-bit integers. While some may argue that a 64-bit integer, which can store integers ranging from zero to 264, is enough to count the grains of sand on Earth, we realized we need to go beyond this limit if we want to be able to store all kinds of transactions adequately. Let’s find out why.

To represent numbers (and to be able to do math with them), computers need to encode this number in a binary system which, depending on the range and the kind of number, requires a certain amount of bits (each bit can be either 0 or 1). For example, integers (whole numbers) ranging from -128 to 127 can be represented with only 8 bits, but if we don’t need negative numbers, we can use the same bits to represent any integer from 0 to 255, and that’s a byte! Larger numbers require more bits, for example, 16-bit, 32-bit, and 64-bit numbers are the most common.

You may have noticed that we are talking about money as whole numbers and not as decimal numbers or cents. Things get more complicated with fractional numbers, which can be encoded using floating point numbers. While binary floating point may be fine for other calculations, they cannot accurately express decimal numbers. This is the same kind of problem that we humans have when we try to represent ⅓ in decimal as 0.33333…, computers have to represent ¹⁄₁₀ in binary!

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