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3 Numerical MethodsAreas3.1 Arithmetics and Error Measures
Figure 3.1.1 (See in context.)
\begin{picture}(152.0,38.0)(-1.0,-1.0)\put(0.0,31.0){\makebox(2.0,6.0)[]{% \small 1}}\put(0.0,26.0){\framebox(2.0,6.0)[]{$s$}}\put(3.0,31.0){\makebox(8.0% ,6.0)[]{\small 8}}\put(3.0,26.0){\framebox(8.0,6.0)[]{$E$}}\put(12.0,31.0){% \makebox(23.0,6.0)[]{\small 23 bits}}\put(12.0,26.0){\framebox(23.0,6.0)[]{$f$% }}\put(133.0,31.0){$N=32$,}\put(135.0,27.0){$p=24$}\put(0.0,18.0){\makebox(2.0% ,6.0)[]{\small 1}}\put(0.0,13.0){\framebox(2.0,6.0)[]{$s$}}\put(3.0,18.0){% \makebox(11.0,6.0)[]{\small 11}}\put(3.0,13.0){\framebox(11.0,6.0)[]{$E$}}\put% (15.0,18.0){\makebox(52.0,6.0)[]{\small 52 bits}}\put(15.0,13.0){\framebox(52.% 0,6.0)[]{$f$}}\put(133.0,17.0){$N=64$,}\put(135.0,13.0){$p=53$}\put(0.0,5.0){% \makebox(2.0,6.0)[]{\small 1}}\put(0.0,0.0){\framebox(2.0,6.0)[]{$s$}}\put(3.0% ,5.0){\makebox(15.0,6.0)[]{\small 15}}\put(3.0,0.0){\framebox(15.0,6.0)[]{$E$}% }\put(19.0,5.0){\makebox(112.0,6.0)[]{\small 112 bits}}\put(19.0,0.0){% \framebox(112.0,6.0)[]{$f$}}\put(133.0,4.0){$N=128$,}\put(135.0,0.0){$p=113$}\end{picture}
Figure 3.1.1: Floating-point arithmetic. Representation of data in the binary interchange formats for binary32, binary64 and binary128 (previously single, double and quad precision).
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Annotations:
Symbols:
s: sign, p: number of significant bits, E: exponent, f: fractional part and N: number of bits in floating point
Permalink:
http://dlmf.nist.gov/3.1.F1.mag
Encodings:
Magnified png, TeX
Modification (effective with 1.0.25):
The figure has been expanded to include the binary128 floating-point representation of data in the binary interchange format described in the 2019 Floating-Point Arithmetic Standard IEEE 754-2019 IEEE (2019). The figure caption has been updated using the terminology of the 2019 Floating-Point Arithmetic Standard.

Suggested 2019-02-22 by Nicola Torracca

See also:
Annotations for §3.1 and Ch.3
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