diff --git a/embedded_c_book/Self_Checking/copy.tex b/embedded_c_book/Self_Checking/copy.tex
index b5a9937..8523181 100644
--- a/embedded_c_book/Self_Checking/copy.tex
+++ b/embedded_c_book/Self_Checking/copy.tex
@@ -1,31 +1,49 @@
 
 
+\section{Variables Bounds checks}
 
-copy.tex
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+Variables read are often expected to fall within a certain range.
+A voltage reading for instance might be expected to be, say 2.5V.
+It may be necessary to check this periodically.
+Because of niose and acceptable drift factors of components as they age
+expecting it to read exactly 2.5V would be impractical, and would
+probably cause a nuisance failure at some time in the future.
 
+The solution to this is to apply a range, or a plus minus acceptable value.
+
+$$ diff = signal - expected $$
+
+The absolute value of this difference can be used and compared to
+the acceptable range.
+
+The C ABS macro is useful for this.
+
+\begin{verbatim}
+ #define ABS(x) if (x > 0) : (x) : (-x)
+\end{verbatim}
+
+Care must be taken however when passing parameters.
+
+For instance this may look acceptable in C
+
+\begin{verbatim}
+ if (ABS(signal - expected) > THRESHOLD )
+    raise_error();
+\end{verbatim}
+
+It expands to
+
+\begin{verbatim}
+  if ( signal - expected ? (signal - expected) : -(signal - expected) > THRESHOLD )
+     raise_error();
+\end{verbatim}
+
+What ths has done is put \textbf{-(signal - expected) > THRESHOLD} as the final argument to the macro.
+
+The C operator greater than, $>$, binds higher than than $?:$ so the results you will get will
+not be what you expect. The correct way to perform  put the ABS call in brackets.
+
+\begin{verbatim}
+ if ( (ABS(signal - expected)) > THRESHOLD )
+    raise_error();
+\end{verbatim}
\ No newline at end of file
diff --git a/embedded_c_book/book.tex b/embedded_c_book/book.tex
index bad09bc..c7879d9 100644
--- a/embedded_c_book/book.tex
+++ b/embedded_c_book/book.tex
@@ -73,8 +73,10 @@
 %\typeout{>>--------------------->> introduction}
 \chapter{Introduction}
 \input{CH1_introduction/copy}
+
 \chapter{Self Checking}
 \input{Self_Checking/copy}
+
 \chapter{Monitors and instrument loops}
 \input{Monitors_intrument_loops/copy}
 \chapter{Binary Scaling}
diff --git a/papers/JOURNAL_fmea_sw_hw/sw_hw_fmea.tex b/papers/JOURNAL_fmea_sw_hw/sw_hw_fmea.tex
index 974cabd..5c99f35 100644
--- a/papers/JOURNAL_fmea_sw_hw/sw_hw_fmea.tex
+++ b/papers/JOURNAL_fmea_sw_hw/sw_hw_fmea.tex
@@ -413,7 +413,7 @@ For instance should  the signal path be followed, with all components encountere
 \paragraph{Exhaustive Single Failure FMEA.}
 %\fmmdglossXFMEA
 %
-To XFMEA, every possible interaction
+To perform XFMEA, every possible interaction
 of a failure mode with all other components in a system would have to be examined. 
 %
 Or in other words, all possible failure scenarios considered.
@@ -449,14 +449,14 @@ double failure scenarios (for burner lock-out scenarios).}
 Where $RD_{double}$ is the reasoning~distance for double failure scenarios:
 \begin{equation}
   \label{eqn:fmea_double}
-  RD_{double} = N.(N-1).(N-2).f  . % \\
+  RD_{double} = N.(N-1).(N-2).{f}^{2}% \\
   %(N^2 - N).f 
 \end{equation}
 % 
 For a theoretical system with 100 components and a fixed 3 failure modes each, this gives reasoning distance of
-$100 \times 99 \times 98 \times 3 = 2,910,600$. % failure mode scenarios.
+$100 \times 99 \times 98 \times 9 = 8,731,800  $. % failure mode scenarios.
 %
-In practise there is an additional complication here, that of 
+In practise there is an additional complication; that of 
 the circuit topology changes that {\fms} can cause.
 
 \paragraph{Reliance on experts for meaningful FMEA Analysis.}