Metrohm 840 PC Control 5.0 / Touch Control - Manual (Page 336)

6.8 Arithmetic algorithms in the Titrando
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PC Control / Touch Control
6.8 Arithmetic algorithms in the Titrando
Some of the algorithms and number formats used in the instrument
software are explained subsequently.
Number format
The standard IEEE 754 (1985) for binary floating-point arithmetic has
been implemented in the software as "single precision" (32 Bit).
Rounding method
Measured values and results are displayed rounded, depending on
user settings. For that purpose, arithmetic rounding is carried out ac-
cording to the following method:
Example for rounding to n = 3 decimal places:
1. 99.644499
99644.499
2. 99644.499 99644.999
3. 99644.499 99644
4. 99644 99.644
Statistics
The arithmetic mean value as well as the absolute and relative standard
deviation are calculated for results R, endpoints EP and variables C:
A maximum of nine results with 20 determinations each at the most can
be evaluated statistically out of a determination.
The following convention applies to the subsequent formulas:
1 ≤ n ≤ 20
1 ≤ k ≤ 9
Mean value
k
x :
∑
=
⋅ =
n
1 i
i, k k
R
n
1
x
Absolute standard deviation S abs
k
:
( )
1 n
x R
abs S
n
1 i
2
k i, k
k −
−
+ =
∑
=
Relative standard deviation S rel
k
(in %):
k
k
k x
abs S
100 rel S ⋅ =
⋅ 10 n
cut
⋅ 10 -n
+ 0.5