[programming] add solutions for parts of exercise, add question

programming/exercises/boolean_logical_indexing.tex

@@ -14,7 +14,7 @@
 %%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry}
 \pagestyle{headandfoot} \header{{\bfseries\large Exercise 4
-    }}{{\bfseries\large Boolean Expressions and logical indexing}}{{\bfseries\large 23. Oktober, 2018}}
+    }}{{\bfseries\large Boolean expressions and logical indexing}}{{\bfseries\large 29. Oktober, 2019}}
 \firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email:
   jan.grewe@uni-tuebingen.de} \runningfooter{}{\thepage}{}
 
@@ -50,24 +50,75 @@ following pattern: ``variables\_datatypes\_\{lastname\}.m''
   \verb+y = [5 2 2 6 0 0 2]+. Execute the following commands and explain.
   \begin{parts}
     \part \verb+x > y+
+    \begin{solution}
+      Returns a vector of zeros and ones. The vector is one for each
+      position at which the value of x is larger than the
+      respective counterpart in y.
+    \end{solution}
     \part \verb+y < x+
+    \begin{solution}
+      same result, because we are inverting the expression.
+    \end{solution}
     \part \verb+x == y+
+    \begin{solution}
+      only 1 for same values in x and y
+    \end{solution}
     \part \verb+x ~= y+
+    \begin{solution}
+      1 for all indices where x and y values are not the same.
+    \end{solution}
     \part \verb+x & ~y+
+    \begin{solution}
+      1 only for the indices in which x is ~= 0 AND y is 0.
+      Implicit conversion of the values in x and y to logicals.
+    \end{solution}
     \part \verb+x | y+
+    \begin{solution}
+      1 at the indices where x or y are ~= 0.
+    \end{solution}
   \end{parts}
 
+  \question What is the difference between the logical operators
+  \verb+&+ and \verb+&&+ and \verb+|+ and \verb+||+ and why are they
+  useful?
+  \begin{solution}
+    \verb+&&+ and \verb+||+ are called short-ciruit AND and OR. In
+    case of an AND expression, the right-hand side is only evaluated
+    if the left-hand side yields \verb+true+. Similarly for OR, the
+    right-hand side is only evaluated if the left-hand side yields
+    \verb+false+.
+
+    Saves processing time.
+  \end{solution}
+  
   \question Find out what the functions \verb+bitand+ and \verb+bitor+ do.
   \begin{parts}
     \part Execute and explain: \verb+bitand(10, 8)+
+    \begin{solution}
+      compares the binary patterns of both numbers with a logican AND
+      and returns the decimal value of the resulting binary pattern.
+      The only bit that is ``on'' for both numbers is the '8', the
+      result is thus '8'.
+    \end{solution}
     \part Execute and explain: \verb+bitor(10, 8)+
+    \begin{solution}
+      Comparison with a logical OR. 8 and 2 bits are ``on'' in at
+      least one of the two binary patterns, the result will be 10.
+    \end{solution}
   \end{parts}
 \item Implement the following Boolean expressions. Test your
   implementations using random integer
   numbers for \verb+x+ and \verb+y+ (\verb+randi+).
   \begin{parts}
     \part The result should be \verb+true+ if \verb+x+ is greater than \verb+y+ and the sum of \verb+x+ and \verb+y+ is not less than 100.
+    \begin{solution}
+      \code{x > y \&  (x+y) >= 100}
+    \end{solution}
     \part The result should be \verb+true+ if \verb+x+ and \verb+y+ are not equal zero or \verb+x+ and \verb+y+ are equal.
+    \begin{solution}
+      \code{(x ~= 0  \&  y ~= 0) | x == y}
+    \end{solution}
+
   \end{parts}
 \end{questions}