Template:Hex
This template shows the exact value of a number of type float.
The significand is given in hexadecimal format, which, apart from the sign, consists of a fixed "1.", followed by 13 hexadecimal characters.
Denormal numbers are shown in normalized format, not in internal format, but without inherently zero digits.
No distinction is made between 0 and -0.
For numbers of type integer which are not exactly representable as float the integer is rounded to float. If an integer just below 2^n is rounded to 2^n the result is shown in the form 2*2^(n-1), thus giving the exponent the value it would have in an exact floating-point representation (which would require up to 10 bits more, hence up to three hexadecimal digits more).
See also Manual:Floating-point errors in expr parser function.
Examples
[edit]{{hex}}→{{hex|a}}→a{{hex|0}}→0{{hex|-0}}→0{{hex|1/7}}→1.2492492492492hex*2^-3{{hex|-2/3}}→-1.5555555555555hex*2^-1{{hex|123}}→1.ec00000000000hex*2^6{{hex|.0123}}→1.930be0ded288dhex*2^-7
{{hex|1+2^-52}}→1.0000000000001hex*2^0{{hex|1.0000000000000002}}→1.0000000000001hex*2^0{{hex|1+2e-16}}→1.0000000000001hex*2^0
{{hex|-1e309}}→-INF{{hex|1e309}}→INF{{hex|1e308}}→1.1ccf385ebc8a0hex*2^1023{{hex|1e307}}→1.c7b1f3cac7433hex*2^1019{{hex|1e306}}→1.6c8e5ca239029hex*2^1016{{hex|1e305}}→1.23a516e82d9bahex*2^1013{{hex|1e304}}→1.d2a1be4048f90hex*2^1009{{hex|1e303}}→1.754e31cd072dahex*2^1006{{hex|1e302}}→1.2aa4f4a405be2hex*2^1003{{hex|1e301}}→1.ddd4baa009303hex*2^999{{hex|1e300}}→1.7e43c8800759chex*2^996{{hex|1e299}}→1.31cfd3999f7b0hex*2^993{{hex|1e298}}→1.e94c85c298c4chex*2^989{{hex|1e297}}→1.87706b0213d0ahex*2^986{{hex|1e296}}→1.3926bc01a973bhex*2^983{{hex|1e295}}→1.f50ac6690f1f8hex*2^979{{hex|1e294}}→1.90d56b873f4c7hex*2^976{{hex|1e293}}→1.40aabc6c32a38hex*2^973{{hex|1e292}}→1.008896bcf54fahex*2^970
{{hex|1e-308}}→1.cc359e067a348hex*2^-1024{{hex|1e-309}}→1.702ae4d1fb5ehex*2^-1027{{hex|1e-310}}→1.2688b70e62bhex*2^-1030{{hex|1e-311}}→1.d74124e3d1hex*2^-1034{{hex|1e-312}}→1.7900ea4fd8hex*2^-1037{{hex|1e-313}}→1.2d9a550cchex*2^-1040{{hex|1e-314}}→1.e2908814hex*2^-1044{{hex|1e-315}}→1.820d39ahex*2^-1047{{hex|1e-316}}→1.34d761hex*2^-1050{{hex|1e-317}}→1.ee257hex*2^-1054{{hex|1e-318}}→1.8b510hex*2^-1057{{hex|1e-319}}→1.3c40hex*2^-1060{{hex|1e-320}}→1.fa0hex*2^-1064{{hex|1e-321}}→1.94hex*2^-1067{{hex|1e-322}}→1.4hex*2^-1070{{hex|1e-323}}→1.0hex*2^-1073{{hex|1e-323/2}}→1.hex*2^-1074{{hex|1e-323/3}}→1.hex*2^-1074{{hex|1e-323/4}}→0{{hex|.{{loop|323|0}}25}}→1.hex*2^-1074{{hex|.{{loop|323|0}}24}}→0{{hex|1000000e-324}}→0
{{hex|1.71*2^-1021}}→1.b5c28f5c28f5chex*2^-1021{{hex|1.71*2^-1022}}→1.b5c28f5c28f5chex*2^-1022{{hex|1.71*2^-1023}}→1.b5c28f5c28f5chex*2^-1023{{hex|1.71*2^-1024}}→1.b5c28f5c28f5chex*2^-1024{{hex|1.71*2^-1025}}→1.b5c28f5c28f60hex*2^-1025{{hex|1.71*2^-1064}}→1.b5chex*2^-1064{{hex|1.71*2^-1065}}→1.b60hex*2^-1065{{hex|1.71*2^-1066}}→1.b6hex*2^-1066{{hex|1.71*2^-1067}}→1.b6hex*2^-1067{{hex|1.71*2^-1068}}→1.b4hex*2^-1068{{hex|1.71*2^-1069}}→1.b8hex*2^-1069{{hex|1.71*2^-1070}}→1.bhex*2^-1070{{hex|1.71*2^-1071}}→1.chex*2^-1071{{hex|1.71*2^-1072}}→1.chex*2^-1072{{hex|1.71*2^-1073}}→1.8hex*2^-1073{{hex|1.71*2^-1074}}→1.0hex*2^-1073{{hex|3*2^-1074}}→1.8hex*2^-1073{{hex|2*2^-1074}}→1.0hex*2^-1073{{hex|1*2^-1074}}→1.hex*2^-1074
Numbers of type integer which are not exactly representable as float:
{{hex|trunc(2^62-512)+trunc511}}→2hex*2^61