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  "body": "\n## Summary\n\nIEEE 754 is the technical standard for [[floating-point arithmetic|RTKRSC3KPH]] used by almost all modern processors.\nIt fixes the binary formats, such as single precision and double precision, and how their bits encode sign, exponent and significand.\nIt requires the basic operations to be correctly rounded, and it defines special values: signed zeros, infinities, NaN and [[subnormal numbers|DHXXSN12JC]].\nBecause of it, the same floating-point program gives the same results on different machines, which makes error analysis portable.\n\n## Explanations\n\n### L1 human\n\nBefore the standard, each computer maker had its own way of storing real numbers, and the same program could give different answers on different machines.\nIEEE 754 is the agreement that settled this.\nA double-precision number uses $64$ bits: $1$ bit for the sign, $11$ bits for the exponent and $52$ bits for the fraction.\nThis gives about $16$ significant decimal digits and numbers up to about $1.8 \\times 10^{308}$.\nIt also says what $1/0$ is (infinity) and what $0/0$ is (NaN, \"not a number\"), so a computation does not simply crash.\n",
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