diff --git a/20220329/alu2.pdf b/20220329/alu2.pdf
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diff --git a/20220329/logo-hochschule-bochum-cvh-text-v2.pdf b/20220329/logo-hochschule-bochum-cvh-text-v2.pdf
new file mode 120000
index 0000000000000000000000000000000000000000..4aa99b8f81061aca6dcaf43eed2d9efef40555f8
--- /dev/null
+++ b/20220329/logo-hochschule-bochum-cvh-text-v2.pdf
@@ -0,0 +1 @@
+../common/logo-hochschule-bochum-cvh-text-v2.pdf
\ No newline at end of file
diff --git a/20220329/logo-hochschule-bochum.pdf b/20220329/logo-hochschule-bochum.pdf
new file mode 120000
index 0000000000000000000000000000000000000000..b6b9491e370e499c9276918182cdb82cb311bcd1
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+++ b/20220329/logo-hochschule-bochum.pdf
@@ -0,0 +1 @@
+../common/logo-hochschule-bochum.pdf
\ No newline at end of file
diff --git a/20220329/pgslides.sty b/20220329/pgslides.sty
new file mode 120000
index 0000000000000000000000000000000000000000..5be1416f4216f076aa268901f52a15d775e43f64
--- /dev/null
+++ b/20220329/pgslides.sty
@@ -0,0 +1 @@
+../common/pgslides.sty
\ No newline at end of file
diff --git a/20220329/pst-circ-pg.sty b/20220329/pst-circ-pg.sty
new file mode 120000
index 0000000000000000000000000000000000000000..81253a45bded27ed7cf1b13b967ae54772b0807d
--- /dev/null
+++ b/20220329/pst-circ-pg.sty
@@ -0,0 +1 @@
+../common/pst-circ-pg.sty
\ No newline at end of file
diff --git a/20220329/rtech-20220329-fig1.pdf b/20220329/rtech-20220329-fig1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..3da36a6cd472dfa5f9a59c6ad251807ee40ade37
Binary files /dev/null and b/20220329/rtech-20220329-fig1.pdf differ
diff --git a/20220329/rtech-20220329-fig1.tex b/20220329/rtech-20220329-fig1.tex
new file mode 100644
index 0000000000000000000000000000000000000000..354733b0c2c7e27449de083f298adee7c37e13cd
--- /dev/null
+++ b/20220329/rtech-20220329-fig1.tex
@@ -0,0 +1,17 @@
+\documentclass{article}
+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
+ \psset{unit=0.6cm}
+ \psset{linewidth=0.03}
+ \begin{pspicture}(-3,-2)(3,2)
+ \logic[logicType=and](-0.75,-0.125){and1}
+ \psline[arrows=o-](-2,0|and12)(and12)
+ \uput[180](-2,0|and12){A}
+ \psline[arrows=o-](-2,0|and11)(and11)
+ \uput[180](-2,0|and11){B}
+ \psline[arrows=o-](2,0|and1Q)(and1Q)
+ \uput[0](2,0|and1Q){Q}
+ \end{pspicture}
+
+\end{document}
diff --git a/20220329/rtech-20220329-fig10.pdf b/20220329/rtech-20220329-fig10.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..37954fe61d3a2e1858fa29531a278820546cd381
Binary files /dev/null and b/20220329/rtech-20220329-fig10.pdf differ
diff --git a/20220329/rtech-20220329-fig10.tex b/20220329/rtech-20220329-fig10.tex
new file mode 100644
index 0000000000000000000000000000000000000000..48c438ff5eaf1ecea39d07309d9364c08ce2d61b
--- /dev/null
+++ b/20220329/rtech-20220329-fig10.tex
@@ -0,0 +1,22 @@
+\documentclass{article}
+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
+ \psset{unit=0.6cm}
+ \psset{linewidth=0.03}
+ \begin{pspicture}(-4,-4)(4,4)
+ \logic[logicType=nand](-0.75,2){nand1}
+ \logic[logicType=nand](-0.75,-2){nand2}
+ \psline[arrows=o-](-3,0|nand12)(nand12)
+ \uput[180](-3,0|nand12){$\overline{\mbox{S}}$}
+ \psline[arrows=o-](-3,0|nand21)(nand21)
+ \uput[180](-3,0|nand21){$\overline{\mbox{R}}$}
+ \psline[arrows=o-](3,0|nand1Q)(nand1Q)
+ \uput[0](3,0|nand1Q){Q}
+ \psline[arrows=o-](3,0|nand2Q)(nand2Q)
+ \uput[0](3,0|nand2Q){$\overline{\mbox{Q}}$}
+ \psline[arrows=*-](2,0|nand1Q)(2,1.75)(-2,0.75)(-2,0|nand22)(nand22)
+ \psline[arrows=*-](2,0|nand2Q)(2,0.75)(-2,1.75)(-2,0|nand11)(nand11)
+ \end{pspicture}
+
+\end{document}
diff --git a/20220329/rtech-20220329-fig11.pdf b/20220329/rtech-20220329-fig11.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..fe828bf67220bf9ee07222e37cc4e51e97491c31
Binary files /dev/null and b/20220329/rtech-20220329-fig11.pdf differ
diff --git a/20220329/rtech-20220329-fig11.tex b/20220329/rtech-20220329-fig11.tex
new file mode 100644
index 0000000000000000000000000000000000000000..9f924ad41052fec1559a37a797ee73df61b116f0
--- /dev/null
+++ b/20220329/rtech-20220329-fig11.tex
@@ -0,0 +1,15 @@
+\documentclass{article}
+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
+ \psset{unit=0.6cm}
+ \psset{linewidth=0.03}
+ \begin{pspicture}(-4,-4)(4,4)
+ \pnode(0,0.5){A}
+ \pnode(0,-0.5){B}
+ \capacitor(A)(B){}
+ \psline[arrows=-o](A)(A|0,1)
+ \psline[arrows=-o](B)(B|0,-1)
+ \end{pspicture}
+
+\end{document}
diff --git a/20220329/rtech-20220329-fig12.pdf b/20220329/rtech-20220329-fig12.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..8e8c32abe6f54d4a29bbb21d4d5e59ea5fdffbe3
Binary files /dev/null and b/20220329/rtech-20220329-fig12.pdf differ
diff --git a/20220329/rtech-20220329-fig12.tex b/20220329/rtech-20220329-fig12.tex
new file mode 100644
index 0000000000000000000000000000000000000000..48c438ff5eaf1ecea39d07309d9364c08ce2d61b
--- /dev/null
+++ b/20220329/rtech-20220329-fig12.tex
@@ -0,0 +1,22 @@
+\documentclass{article}
+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
+ \psset{unit=0.6cm}
+ \psset{linewidth=0.03}
+ \begin{pspicture}(-4,-4)(4,4)
+ \logic[logicType=nand](-0.75,2){nand1}
+ \logic[logicType=nand](-0.75,-2){nand2}
+ \psline[arrows=o-](-3,0|nand12)(nand12)
+ \uput[180](-3,0|nand12){$\overline{\mbox{S}}$}
+ \psline[arrows=o-](-3,0|nand21)(nand21)
+ \uput[180](-3,0|nand21){$\overline{\mbox{R}}$}
+ \psline[arrows=o-](3,0|nand1Q)(nand1Q)
+ \uput[0](3,0|nand1Q){Q}
+ \psline[arrows=o-](3,0|nand2Q)(nand2Q)
+ \uput[0](3,0|nand2Q){$\overline{\mbox{Q}}$}
+ \psline[arrows=*-](2,0|nand1Q)(2,1.75)(-2,0.75)(-2,0|nand22)(nand22)
+ \psline[arrows=*-](2,0|nand2Q)(2,0.75)(-2,1.75)(-2,0|nand11)(nand11)
+ \end{pspicture}
+
+\end{document}
diff --git a/20220329/rtech-20220329-fig2.pdf b/20220329/rtech-20220329-fig2.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..41aa42087e384f2296c09007a9e1658469e852f3
Binary files /dev/null and b/20220329/rtech-20220329-fig2.pdf differ
diff --git a/20220329/rtech-20220329-fig2.tex b/20220329/rtech-20220329-fig2.tex
new file mode 100644
index 0000000000000000000000000000000000000000..354733b0c2c7e27449de083f298adee7c37e13cd
--- /dev/null
+++ b/20220329/rtech-20220329-fig2.tex
@@ -0,0 +1,17 @@
+\documentclass{article}
+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
+ \psset{unit=0.6cm}
+ \psset{linewidth=0.03}
+ \begin{pspicture}(-3,-2)(3,2)
+ \logic[logicType=and](-0.75,-0.125){and1}
+ \psline[arrows=o-](-2,0|and12)(and12)
+ \uput[180](-2,0|and12){A}
+ \psline[arrows=o-](-2,0|and11)(and11)
+ \uput[180](-2,0|and11){B}
+ \psline[arrows=o-](2,0|and1Q)(and1Q)
+ \uput[0](2,0|and1Q){Q}
+ \end{pspicture}
+
+\end{document}
diff --git a/20220329/rtech-20220329-fig3.pdf b/20220329/rtech-20220329-fig3.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..4386026e7996aba10f474e6df7895a9b42275d7c
Binary files /dev/null and b/20220329/rtech-20220329-fig3.pdf differ
diff --git a/20220329/rtech-20220329-fig3.tex b/20220329/rtech-20220329-fig3.tex
new file mode 100644
index 0000000000000000000000000000000000000000..354733b0c2c7e27449de083f298adee7c37e13cd
--- /dev/null
+++ b/20220329/rtech-20220329-fig3.tex
@@ -0,0 +1,17 @@
+\documentclass{article}
+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
+ \psset{unit=0.6cm}
+ \psset{linewidth=0.03}
+ \begin{pspicture}(-3,-2)(3,2)
+ \logic[logicType=and](-0.75,-0.125){and1}
+ \psline[arrows=o-](-2,0|and12)(and12)
+ \uput[180](-2,0|and12){A}
+ \psline[arrows=o-](-2,0|and11)(and11)
+ \uput[180](-2,0|and11){B}
+ \psline[arrows=o-](2,0|and1Q)(and1Q)
+ \uput[0](2,0|and1Q){Q}
+ \end{pspicture}
+
+\end{document}
diff --git a/20220329/rtech-20220329-fig4.pdf b/20220329/rtech-20220329-fig4.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..57ae1091dc6fdcf138cd5af5240dcf5917cc0c6e
Binary files /dev/null and b/20220329/rtech-20220329-fig4.pdf differ
diff --git a/20220329/rtech-20220329-fig4.tex b/20220329/rtech-20220329-fig4.tex
new file mode 100644
index 0000000000000000000000000000000000000000..76707503d44cec7e4574a43ec87615071dcffcdf
--- /dev/null
+++ b/20220329/rtech-20220329-fig4.tex
@@ -0,0 +1,55 @@
+\documentclass{article}
+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
+ \newcommand{\invisible}{\tiny\color{white}}
+ \psset{logicLabelstyle=\invisible}
+ \newcommand{\logicSymbol}{\small\boldmath\bf\rule{0pt}{0.5cm}}
+ \psset{logicSymbolstyle=\logicSymbol}
+ \psset{unit=0.6cm}
+ \psset{linewidth=0.03}
+ \begin{pspicture}(-3,-2)(3,2)
+ \pnode(-1,1.5){A}
+ \uput[l](-2.5,0|A){$S$}
+ \pnode(1,1.5){B}
+ \ground[connectingdot=false](2,1.5)
+ \relais(A)(B){}
+ \pnode(2.5,2.5){A3}
+ \uput[l](2.0,0|A3){$R$}
+ \pnode(4.5,2.5){B3}
+ \ground[connectingdot=false](5.5,2.5)
+ \relais(A3)(B3){}
+ \pnode(-0.5,0){C0}
+ \psline[arrows=-*](C0)(-1.5,0)(-1.5,1.5)
+ \pnode(0.5,0.3){D0}
+ \pnode(0.5,-0.3){E0}
+ \pnode(3,-0.3){C3}
+ \pnode(4,0){D3}
+ \pnode(4,-0.6){E3}
+ \psline[arrows=*-,linewidth=2\pslinewidth](C3)(D3)
+ \pnode(7,0.7){D3plus}
+ \uput[180](D3plus){\textbf{+}}
+ \psline(E0)(C3)
+ \psline[arrows=->,arrowsize=0.3](D3)(D3plus|D3)(D3plus)
+ \psline[arrows=*-,linewidth=2\pslinewidth](C0)(D0)
+ \pnode(-0.5,-1.5){C1}
+ \pnode(0.5,-1.2){D1}
+ \pnode(0.5,-1.8){E1}
+ \uput[r](2.5,0|E1){$Q$}
+ \pnode(-3.0,-0.5){C1plus}
+ \uput[180](C1plus){\textbf{+}}
+ \psline[arrows=->,arrowsize=0.3](C1)(C1plus|C1)(C1plus)
+ \psline[arrows=*-,linewidth=2\pslinewidth](C1)(D1)
+ \psline[linestyle=dashed](0,-1.25)(0,1.0)
+ \psline[linestyle=dashed](3.5,-0.15)(3.5,2.0)
+ \psline[arrows=o-](-2.5,0|A)(A)
+ \psline[arrows=o-](2.0,0|A3)(A3)
+ \psline(B)(2,0|B)
+ \psline(B3)(5.5|B3)
+ \psline[arrows=o-](1.5,0|D0)(D0)
+ \psline[arrows=o-](1.5,0|D1)(D1)
+ \psline[arrows=o-](2.5,0|E1)(E1)
+ \psline[arrows=o-](5.0,0|E3)(E3)
+ \end{pspicture}
+
+\end{document}
diff --git a/20220329/rtech-20220329-fig5.pdf b/20220329/rtech-20220329-fig5.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..9a0b5daa4372f38123e58181647b5f0843e150b8
Binary files /dev/null and b/20220329/rtech-20220329-fig5.pdf differ
diff --git a/20220329/rtech-20220329-fig5.tex b/20220329/rtech-20220329-fig5.tex
new file mode 100644
index 0000000000000000000000000000000000000000..76707503d44cec7e4574a43ec87615071dcffcdf
--- /dev/null
+++ b/20220329/rtech-20220329-fig5.tex
@@ -0,0 +1,55 @@
+\documentclass{article}
+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
+ \newcommand{\invisible}{\tiny\color{white}}
+ \psset{logicLabelstyle=\invisible}
+ \newcommand{\logicSymbol}{\small\boldmath\bf\rule{0pt}{0.5cm}}
+ \psset{logicSymbolstyle=\logicSymbol}
+ \psset{unit=0.6cm}
+ \psset{linewidth=0.03}
+ \begin{pspicture}(-3,-2)(3,2)
+ \pnode(-1,1.5){A}
+ \uput[l](-2.5,0|A){$S$}
+ \pnode(1,1.5){B}
+ \ground[connectingdot=false](2,1.5)
+ \relais(A)(B){}
+ \pnode(2.5,2.5){A3}
+ \uput[l](2.0,0|A3){$R$}
+ \pnode(4.5,2.5){B3}
+ \ground[connectingdot=false](5.5,2.5)
+ \relais(A3)(B3){}
+ \pnode(-0.5,0){C0}
+ \psline[arrows=-*](C0)(-1.5,0)(-1.5,1.5)
+ \pnode(0.5,0.3){D0}
+ \pnode(0.5,-0.3){E0}
+ \pnode(3,-0.3){C3}
+ \pnode(4,0){D3}
+ \pnode(4,-0.6){E3}
+ \psline[arrows=*-,linewidth=2\pslinewidth](C3)(D3)
+ \pnode(7,0.7){D3plus}
+ \uput[180](D3plus){\textbf{+}}
+ \psline(E0)(C3)
+ \psline[arrows=->,arrowsize=0.3](D3)(D3plus|D3)(D3plus)
+ \psline[arrows=*-,linewidth=2\pslinewidth](C0)(D0)
+ \pnode(-0.5,-1.5){C1}
+ \pnode(0.5,-1.2){D1}
+ \pnode(0.5,-1.8){E1}
+ \uput[r](2.5,0|E1){$Q$}
+ \pnode(-3.0,-0.5){C1plus}
+ \uput[180](C1plus){\textbf{+}}
+ \psline[arrows=->,arrowsize=0.3](C1)(C1plus|C1)(C1plus)
+ \psline[arrows=*-,linewidth=2\pslinewidth](C1)(D1)
+ \psline[linestyle=dashed](0,-1.25)(0,1.0)
+ \psline[linestyle=dashed](3.5,-0.15)(3.5,2.0)
+ \psline[arrows=o-](-2.5,0|A)(A)
+ \psline[arrows=o-](2.0,0|A3)(A3)
+ \psline(B)(2,0|B)
+ \psline(B3)(5.5|B3)
+ \psline[arrows=o-](1.5,0|D0)(D0)
+ \psline[arrows=o-](1.5,0|D1)(D1)
+ \psline[arrows=o-](2.5,0|E1)(E1)
+ \psline[arrows=o-](5.0,0|E3)(E3)
+ \end{pspicture}
+
+\end{document}
diff --git a/20220329/rtech-20220329-fig6.pdf b/20220329/rtech-20220329-fig6.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..b2a93a45507d1af64be71887932cb92bcda71c96
Binary files /dev/null and b/20220329/rtech-20220329-fig6.pdf differ
diff --git a/20220329/rtech-20220329-fig6.tex b/20220329/rtech-20220329-fig6.tex
new file mode 100644
index 0000000000000000000000000000000000000000..48c438ff5eaf1ecea39d07309d9364c08ce2d61b
--- /dev/null
+++ b/20220329/rtech-20220329-fig6.tex
@@ -0,0 +1,22 @@
+\documentclass{article}
+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
+ \psset{unit=0.6cm}
+ \psset{linewidth=0.03}
+ \begin{pspicture}(-4,-4)(4,4)
+ \logic[logicType=nand](-0.75,2){nand1}
+ \logic[logicType=nand](-0.75,-2){nand2}
+ \psline[arrows=o-](-3,0|nand12)(nand12)
+ \uput[180](-3,0|nand12){$\overline{\mbox{S}}$}
+ \psline[arrows=o-](-3,0|nand21)(nand21)
+ \uput[180](-3,0|nand21){$\overline{\mbox{R}}$}
+ \psline[arrows=o-](3,0|nand1Q)(nand1Q)
+ \uput[0](3,0|nand1Q){Q}
+ \psline[arrows=o-](3,0|nand2Q)(nand2Q)
+ \uput[0](3,0|nand2Q){$\overline{\mbox{Q}}$}
+ \psline[arrows=*-](2,0|nand1Q)(2,1.75)(-2,0.75)(-2,0|nand22)(nand22)
+ \psline[arrows=*-](2,0|nand2Q)(2,0.75)(-2,1.75)(-2,0|nand11)(nand11)
+ \end{pspicture}
+
+\end{document}
diff --git a/20220329/rtech-20220329-fig7.pdf b/20220329/rtech-20220329-fig7.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..a4c4478acf001d66894e18e7584edb470600268e
Binary files /dev/null and b/20220329/rtech-20220329-fig7.pdf differ
diff --git a/20220329/rtech-20220329-fig7.tex b/20220329/rtech-20220329-fig7.tex
new file mode 100644
index 0000000000000000000000000000000000000000..9f924ad41052fec1559a37a797ee73df61b116f0
--- /dev/null
+++ b/20220329/rtech-20220329-fig7.tex
@@ -0,0 +1,15 @@
+\documentclass{article}
+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
+ \psset{unit=0.6cm}
+ \psset{linewidth=0.03}
+ \begin{pspicture}(-4,-4)(4,4)
+ \pnode(0,0.5){A}
+ \pnode(0,-0.5){B}
+ \capacitor(A)(B){}
+ \psline[arrows=-o](A)(A|0,1)
+ \psline[arrows=-o](B)(B|0,-1)
+ \end{pspicture}
+
+\end{document}
diff --git a/20220329/rtech-20220329-fig8.pdf b/20220329/rtech-20220329-fig8.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..905f4d59c0b3a729fb46ce11a64e573c99e3d2f0
Binary files /dev/null and b/20220329/rtech-20220329-fig8.pdf differ
diff --git a/20220329/rtech-20220329-fig8.tex b/20220329/rtech-20220329-fig8.tex
new file mode 100644
index 0000000000000000000000000000000000000000..48c438ff5eaf1ecea39d07309d9364c08ce2d61b
--- /dev/null
+++ b/20220329/rtech-20220329-fig8.tex
@@ -0,0 +1,22 @@
+\documentclass{article}
+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
+ \psset{unit=0.6cm}
+ \psset{linewidth=0.03}
+ \begin{pspicture}(-4,-4)(4,4)
+ \logic[logicType=nand](-0.75,2){nand1}
+ \logic[logicType=nand](-0.75,-2){nand2}
+ \psline[arrows=o-](-3,0|nand12)(nand12)
+ \uput[180](-3,0|nand12){$\overline{\mbox{S}}$}
+ \psline[arrows=o-](-3,0|nand21)(nand21)
+ \uput[180](-3,0|nand21){$\overline{\mbox{R}}$}
+ \psline[arrows=o-](3,0|nand1Q)(nand1Q)
+ \uput[0](3,0|nand1Q){Q}
+ \psline[arrows=o-](3,0|nand2Q)(nand2Q)
+ \uput[0](3,0|nand2Q){$\overline{\mbox{Q}}$}
+ \psline[arrows=*-](2,0|nand1Q)(2,1.75)(-2,0.75)(-2,0|nand22)(nand22)
+ \psline[arrows=*-](2,0|nand2Q)(2,0.75)(-2,1.75)(-2,0|nand11)(nand11)
+ \end{pspicture}
+
+\end{document}
diff --git a/20220329/rtech-20220329-fig9.pdf b/20220329/rtech-20220329-fig9.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..86e8e36b628b8c943d1972bae2d810667d6e2ceb
Binary files /dev/null and b/20220329/rtech-20220329-fig9.pdf differ
diff --git a/20220329/rtech-20220329-fig9.tex b/20220329/rtech-20220329-fig9.tex
new file mode 100644
index 0000000000000000000000000000000000000000..9f924ad41052fec1559a37a797ee73df61b116f0
--- /dev/null
+++ b/20220329/rtech-20220329-fig9.tex
@@ -0,0 +1,15 @@
+\documentclass{article}
+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
+ \psset{unit=0.6cm}
+ \psset{linewidth=0.03}
+ \begin{pspicture}(-4,-4)(4,4)
+ \pnode(0,0.5){A}
+ \pnode(0,-0.5){B}
+ \capacitor(A)(B){}
+ \psline[arrows=-o](A)(A|0,1)
+ \psline[arrows=-o](B)(B|0,-1)
+ \end{pspicture}
+
+\end{document}
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+% rtech-20220329.pdf - Lecture Slides on Computer Technology
+% Copyright (C) 2012, 2013, 2014, 2021, 2022 Peter Gerwinski
+%
+% This document is free software: you can redistribute it and/or
+% modify it either under the terms of the Creative Commons
+% Attribution-ShareAlike 3.0 License, or under the terms of the
+% GNU General Public License as published by the Free Software
+% Foundation, either version 3 of the License, or (at your option)
+% any later version.
+%
+% This document is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this document. If not, see <http://www.gnu.org/licenses/>.
+%
+% You should have received a copy of the Creative Commons
+% Attribution-ShareAlike 3.0 Unported License along with this
+% document. If not, see <http://creativecommons.org/licenses/>.
+
+% README: Vom Addierer zum Computer
+
+\documentclass[10pt,t]{beamer}
+
+\usepackage{pgslides}
+\usepackage{pdftricks}
+%\usepackage[obeyfamily=false,mathrm=mathsf,textrm=sffamily]{siunitx}
+%\usepackage{eurosym}
+
+\newrgbcolor{orange}{0.7 0.2 0.0}
+
+\newcommand{\Cin}{C\raisebox{-0.5ex}{\footnotesize in}}
+\newcommand{\Cout}{C\raisebox{-0.5ex}{\footnotesize out}}
+
+\begin{psinputs}
+ \usepackage[latin1]{inputenc}
+ \usepackage[german]{babel}
+ \usepackage[T1]{fontenc}
+ \usepackage{helvet}
+ \renewcommand*\familydefault{\sfdefault}
+ \usepackage{pstricks,pst-grad,pst-circ-pg}
+ \newcommand{\invisible}{\tiny\color{white}}
+ \psset{unit=1cm}
+ \psset{logicLabelstyle=\invisible}
+ \newcommand{\logicSymbol}{\small\boldmath\bf\rule{0pt}{0.5cm}}
+ \psset{logicSymbolstyle=\logicSymbol}
+ \newcommand{\Cin}{C\raisebox{-0.5ex}{\footnotesize in}}
+ \newcommand{\Cout}{C\raisebox{-0.5ex}{\footnotesize out}}
+\end{psinputs}
+
+\title{Rechnertechnik}
+\author{Prof.\ Dr.\ rer.\ nat.\ Peter Gerwinski}
+\date{29.\ März 2022}
+
+\begin{document}
+
+\maketitleframe
+
+\sectionnonumber{\inserttitle}
+
+\begin{frame}
+
+ \showsectionnonumber
+
+ \begin{itemize}
+ \item[\textbf{1}] \textbf{Einführung}
+ \begin{itemize}
+ \item[1.1] Was ist Rechnertechnik?
+ \item[1.2] Was ist ein Computer?
+ \end{itemize}
+ \item[\textbf{2}] \textbf{Vom Schaltkreis zum Computer}
+ \begin{itemize}
+ \item[2.1] Logik-Schaltkreise
+ \item[2.2] Binärdarstellung von Zahlen
+ \item[2.3] Vom Logik-Schaltkreis zum Addierer
+ \color{medgreen}
+ \item[2.4] Negative Zahlen
+ \color{red}
+ \item[2.5] Vom Addierer zum Computer
+ \item[\dots]
+ \end{itemize}
+ \color{gray}
+ \item[\textbf{3}] \textbf{Architekturmerkmale von Prozessoren}
+ \item[\textbf{4}] \textbf{Der CPU-Stack}
+% \item[\textbf{5}] \textbf{Hardwarenahe Programmierung}
+% \item[\textbf{6}] \textbf{Anwender-Software}
+% \item[\textbf{7}] \textbf{Bus-Systeme}
+% \item[\textbf{8}] \textbf{Pipelining}
+ \item[\textbf{\dots\hspace{-0.75em}}]
+% \item[\textbf{9}] \textbf{Ausblick}
+ \end{itemize}
+
+\end{frame}
+
+\setcounter{section}{1}
+\section{Vom Schaltkreis zum Computer}
+\setcounter{subsection}{3}
+\subsection{Negative Zahlen}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Speicher ist begrenzt!\\
+ \textarrow\ feste Anzahl von Bits
+
+ \medskip
+
+ 8-Bit-Zahlen ohne Vorzeichen: \lstinline{uint8_t}\\
+ \textarrow\ Zahlenwerte von \lstinline{0x00} bis \lstinline{0xff} = 0 bis 255\\
+ \pause
+ \textarrow\ 255 + 1 = 0
+
+ \pause
+ \medskip
+
+ 8-Bit-Zahlen mit Vorzeichen: \lstinline{int8_t}\\
+ \lstinline{0xff} = 255 ist die "`natürliche"' Schreibweise für $-1$.\\
+ \pause
+ \textarrow\ Zweierkomplement
+
+ \pause
+ \medskip
+
+ Oberstes Bit = 1: negativ\\
+ Oberstes Bit = 0: positiv\\
+ \textarrow\ 127 + 1 = $-128$
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Speicher ist begrenzt!\\
+ \textarrow\ feste Anzahl von Bits
+
+ \medskip
+
+ 16-Bit-Zahlen ohne Vorzeichen:
+ \lstinline{uint16_t}\hfill\lstinline{uint8_t}\\
+ \textarrow\ Zahlenwerte von \lstinline{0x0000} bis \lstinline{0xffff}
+ = 0 bis 65535\hfill 0 bis 255\\
+ \textarrow\ 65535 + 1 = 0\hfill 255 + 1 = 0
+
+ \medskip
+
+ 16-Bit-Zahlen mit Vorzeichen:
+ \lstinline{int16_t}\hfill\lstinline{int8_t}\\
+ \lstinline{0xffff} = 66535 ist die "`natürliche"' Schreibweise für $-1$.\hfill
+ \lstinline{0xff} = 255 = $-1$\\
+ \textarrow\ Zweierkomplement
+
+ \medskip
+
+ Oberstes Bit = 1: negativ\\
+ Oberstes Bit = 0: positiv\\
+ \textarrow\ 32767 + 1 = $-32768$
+
+ \bigskip
+ Literatur: \url{http://xkcd.com/571/}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Frage: \emph{Für welche Zahl steht der Speicherinhalt\,
+ \raisebox{2pt}{%
+ \tabcolsep0.25em
+ \begin{tabular}{|c|c|}\hline
+ \rule{0pt}{11pt}a3 & 90 \\\hline
+ \end{tabular}}
+ (hexadezimal)?}
+
+ \pause
+ \smallskip
+ Antwort: \emph{Das kommt darauf an.} ;--)
+
+ \pause
+ \medskip
+ Little-Endian:
+
+ \smallskip
+
+ \begin{tabular}{lrl}
+ als \lstinline,int8_t,: & $-93$ & (nur erstes Byte)\\
+ als \lstinline,uint8_t,: & $163$ & (nur erstes Byte)\\
+ als \lstinline,int16_t,: & $-28509$\\
+ als \lstinline,uint16_t,: & $37027$\\
+ \lstinline,int32_t, oder größer: & $37027$
+ & (zusätzliche Bytes mit Nullen aufgefüllt)
+ \end{tabular}
+
+ \pause
+ \medskip
+ Big-Endian:
+
+ \smallskip
+
+ \begin{tabular}{lrl}
+ als \lstinline,int8_t,: & $-93$ & (nur erstes Byte)\\
+ als \lstinline,uint8_t,: & $163$ & (nur erstes Byte)\\
+ als \lstinline,int16_t,: & $-23664$\\
+ als \lstinline,uint16_t,: & $41872$\\ als \lstinline,int32_t,: & $-1550843904$ & (zusätzliche Bytes\\
+ als \lstinline,uint32_t,: & $2744123392$ & mit Nullen aufgefüllt)\\
+ als \lstinline,int64_t,: & $-6660823848880963584$\\
+ als \lstinline,uint64_t,: & $11785920224828588032$\\
+ \end{tabular}
+
+ \vspace*{-1cm}
+
+\end{frame}
+
+\begin{frame}
+
+ \showsubsection
+
+ Aufbau einer Schaltung zum Bilden des Zweierkomplements:\\
+ {\color{red}Sie sind dran.}
+
+ \medskip
+
+ \textarrow\ Siehe: \file{../20220322/2er-komplement-$*$.png}
+
+\end{frame}
+
+\subsection{Vom Addierer zum Computer}
+
+\begin{frame}
+
+ \showsubsection
+
+ Wir können jetzt addieren und subtrahieren.\\
+ Wie bauen wir daraus einen Turing-vollständigen Computer?
+ \begin{itemize}
+ \pause
+ \item
+ Arithmetisch-logische Einheit (ALU)%\\
+% (Skript: Seite 20)
+% \pause
+ \item
+ Speicher
+% \pause
+ \item
+ Takt
+ \end{itemize}
+
+\end{frame}
+
+\iffalse
+
+\begin{frame}
+
+ \showsubsection
+
+ Zeit ins Spiel bringen:
+ \begin{itemize}
+ \item sich 1 Bit merken: Flipflop
+ \item zeitlicher Ablauf: Taktgeber
+ \item voranschreiten: Zähler (aus Flipflops)
+ \end{itemize}
+
+ \pause
+ \bigskip
+
+ Programmieren:
+ \begin{itemize}
+ \item ALU kann verschiedene Operationen durchführen
+ \item Maschinensprache codiert, welche Operation ausgeführt werden soll
+ \item Das Laden von Registern ermöglicht auch Sprünge \textarrow\ Schleifen
+ \end{itemize}
+
+\end{frame}
+
+\fi
+
+\setcounter{subsection}{4}
+\subsection{Vom Addierer zum Computer}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ 1-Bit-Multiplizierer
+ \visible<3->{= Und-Verknüpfung}
+
+ \medskip
+
+ \begin{tabular}{|c|c||c|}\hline
+ A & B & Q \\\hline\hline
+ 0 & 0 & \visible<2->{0} \\\hline
+ 0 & 1 & \visible<2->{0} \\\hline
+ 1 & 0 & \visible<2->{0} \\\hline
+ 1 & 1 & \visible<2->{1} \\\hline
+ \end{tabular}\quad\pause[3]
+ \begin{minipage}{2.5cm}
+ \vspace*{0.5cm}
+ \begin{pdfpic}
+ \psset{unit=0.6cm}
+ \psset{linewidth=0.03}
+ \begin{pspicture}(-3,-2)(3,2)
+ \logic[logicType=and](-0.75,-0.125){and1}
+ \psline[arrows=o-](-2,0|and12)(and12)
+ \uput[180](-2,0|and12){A}
+ \psline[arrows=o-](-2,0|and11)(and11)
+ \uput[180](-2,0|and11){B}
+ \psline[arrows=o-](2,0|and1Q)(and1Q)
+ \uput[0](2,0|and1Q){Q}
+ \end{pspicture}
+ \end{pdfpic}
+ \end{minipage}
+
+\end{frame}
+
+\begin{frame}
+
+ \showsubsection
+
+ 1-Bit-Multiplizierer = Und-Verknüpfung
+
+ \smallskip
+
+ n-Bit-Multiplizierer\pause: "`schriftlich"' multiplizieren
+
+ \bigskip
+ \pause
+
+ Beispiel: $13 \cdot 5$
+
+ \smallskip
+
+ \begin{tabular}{r}
+ $1101 \cdot 101$\\[-1.5\smallskipamount]
+ \rule{2cm}{1pt}\\
+ $1101\phantom{00}$\\
+ $0\phantom{0}$\\
+ $1101$\\[-1.5\smallskipamount]
+ \rule{2cm}{1pt}\\
+ $1000001$
+ \end{tabular}%
+ \begin{picture}(0,0)
+ \put(-0.95,-0.63){\mbox{\scriptsize 1}}
+ \put(-1.15,-0.63){\mbox{\scriptsize 1}}
+ \put(-1.35,-0.63){\mbox{\scriptsize 1}}
+ \put(-1.55,-0.63){\mbox{\scriptsize 1}}
+ \end{picture}\pause
+ \hspace*{2cm}%
+ \begin{minipage}{5cm}
+ Multiplizier-Schaltkreis\\
+ für zwei 2-Bit-Zahlen:\\[\smallskipamount]
+ \color{red}Sie sind dran.
+ \end{minipage}
+
+\end{frame}
+
+\begin{frame}
+
+ \showsubsection
+
+ Schaltkreis, der wahlweise eine von mehreren Verknüpfungen
+ durchführt:
+
+ \smallskip
+
+ \newterm{arithmetisch-logische Einheit\/} --
+ \newterm{arithmetic logic unit (ALU)}
+
+ \bigskip
+
+ \begin{center}
+ \vspace*{-2.5cm}
+ \includegraphics{alu2.pdf}
+ \vspace*{-23cm}
+ \end{center}
+
+ \bigskip
+
+ Siehe z.\,B.: \url{https://en.wikipedia.org/wiki/File:74181aluschematic.png}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \begin{visibleenv}<2->
+ \showsubsection
+
+ Information speichern
+ \end{visibleenv}
+
+ \begin{pdfpic}
+ \newcommand{\invisible}{\tiny\color{white}}
+ \psset{logicLabelstyle=\invisible}
+ \newcommand{\logicSymbol}{\small\boldmath\bf\rule{0pt}{0.5cm}}
+ \psset{logicSymbolstyle=\logicSymbol}
+ \psset{unit=0.6cm}
+ \psset{linewidth=0.03}
+ \begin{pspicture}(-3,-2)(3,2)
+ \pnode(-1,1.5){A}
+ \uput[l](-2.5,0|A){$S$}
+ \pnode(1,1.5){B}
+ \ground[connectingdot=false](2,1.5)
+ \relais(A)(B){}
+ \pnode(2.5,2.5){A3}
+ \uput[l](2.0,0|A3){$R$}
+ \pnode(4.5,2.5){B3}
+ \ground[connectingdot=false](5.5,2.5)
+ \relais(A3)(B3){}
+ \pnode(-0.5,0){C0}
+ \psline[arrows=-*](C0)(-1.5,0)(-1.5,1.5)
+ \pnode(0.5,0.3){D0}
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+ \pnode(4,0){D3}
+ \pnode(4,-0.6){E3}
+ \psline[arrows=*-,linewidth=2\pslinewidth](C3)(D3)
+ \pnode(7,0.7){D3plus}
+ \uput[180](D3plus){\textbf{+}}
+ \psline(E0)(C3)
+ \psline[arrows=->,arrowsize=0.3](D3)(D3plus|D3)(D3plus)
+ \psline[arrows=*-,linewidth=2\pslinewidth](C0)(D0)
+ \pnode(-0.5,-1.5){C1}
+ \pnode(0.5,-1.2){D1}
+ \pnode(0.5,-1.8){E1}
+ \uput[r](2.5,0|E1){$Q$}
+ \pnode(-3.0,-0.5){C1plus}
+ \uput[180](C1plus){\textbf{+}}
+ \psline[arrows=->,arrowsize=0.3](C1)(C1plus|C1)(C1plus)
+ \psline[arrows=*-,linewidth=2\pslinewidth](C1)(D1)
+ \psline[linestyle=dashed](0,-1.25)(0,1.0)
+ \psline[linestyle=dashed](3.5,-0.15)(3.5,2.0)
+ \psline[arrows=o-](-2.5,0|A)(A)
+ \psline[arrows=o-](2.0,0|A3)(A3)
+ \psline(B)(2,0|B)
+ \psline(B3)(5.5|B3)
+ \psline[arrows=o-](1.5,0|D0)(D0)
+ \psline[arrows=o-](1.5,0|D1)(D1)
+ \psline[arrows=o-](2.5,0|E1)(E1)
+ \psline[arrows=o-](5.0,0|E3)(E3)
+ \end{pspicture}
+ \end{pdfpic}
+
+ \pause
+
+ \newterm{Selbsthalteschaltung}
+
+ 1-Bit-\newterm{Speicherzelle}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Information speichern
+
+ \begin{pdfpic}
+ \psset{unit=0.6cm}
+ \psset{linewidth=0.03}
+ \begin{pspicture}(-4,-4)(4,4)
+ \logic[logicType=nand](-0.75,2){nand1}
+ \logic[logicType=nand](-0.75,-2){nand2}
+ \psline[arrows=o-](-3,0|nand12)(nand12)
+ \uput[180](-3,0|nand12){$\overline{\mbox{S}}$}
+ \psline[arrows=o-](-3,0|nand21)(nand21)
+ \uput[180](-3,0|nand21){$\overline{\mbox{R}}$}
+ \psline[arrows=o-](3,0|nand1Q)(nand1Q)
+ \uput[0](3,0|nand1Q){Q}
+ \psline[arrows=o-](3,0|nand2Q)(nand2Q)
+ \uput[0](3,0|nand2Q){$\overline{\mbox{Q}}$}
+ \psline[arrows=*-](2,0|nand1Q)(2,1.75)(-2,0.75)(-2,0|nand22)(nand22)
+ \psline[arrows=*-](2,0|nand2Q)(2,0.75)(-2,1.75)(-2,0|nand11)(nand11)
+ \end{pspicture}
+ \end{pdfpic}
+
+ \newterm{Bistabile Kippstufe} -- \newterm{Bistabiler Multivibrator} -- \newterm{Flip-Flop}
+
+ 1-Bit-Speicherzelle
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Information speichern
+
+ \vspace*{-0.5cm}
+
+ \begin{pdfpic}
+ \psset{unit=0.6cm}
+ \psset{linewidth=0.03}
+ \begin{pspicture}(-4,-4)(4,4)
+ \pnode(0,0.5){A}
+ \pnode(0,-0.5){B}
+ \capacitor(A)(B){}
+ \psline[arrows=-o](A)(A|0,1)
+ \psline[arrows=-o](B)(B|0,-1)
+ \end{pspicture}
+ \end{pdfpic}
+
+ \vspace*{-1.0cm}
+
+ \newterm{Kondensator}
+
+ \only<2->{\newterm{dynamische\/}} 1-Bit-Speicherzelle\\
+ \pause
+ \textarrow\ benötigt \newterm{Refresh}-Schaltung
+
+ \pause[3]
+ \medskip
+ Flip-Flop
+
+ \newterm{statische\/} 1-Bit-Speicherzelle
+
+ \begin{pdfpic}
+ \psset{unit=0.6cm}
+ \psset{linewidth=0.03}
+ \begin{pspicture}(-4,-4)(4,4)
+ \logic[logicType=nand](-0.75,2){nand1}
+ \logic[logicType=nand](-0.75,-2){nand2}
+ \psline[arrows=o-](-3,0|nand12)(nand12)
+ \uput[180](-3,0|nand12){$\overline{\mbox{S}}$}
+ \psline[arrows=o-](-3,0|nand21)(nand21)
+ \uput[180](-3,0|nand21){$\overline{\mbox{R}}$}
+ \psline[arrows=o-](3,0|nand1Q)(nand1Q)
+ \uput[0](3,0|nand1Q){Q}
+ \psline[arrows=o-](3,0|nand2Q)(nand2Q)
+ \uput[0](3,0|nand2Q){$\overline{\mbox{Q}}$}
+ \psline[arrows=*-](2,0|nand1Q)(2,1.75)(-2,0.75)(-2,0|nand22)(nand22)
+ \psline[arrows=*-](2,0|nand2Q)(2,0.75)(-2,1.75)(-2,0|nand11)(nand11)
+ \end{pspicture}
+ \end{pdfpic}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+ \showsubsection
+
+ Computer
+ \begin{itemize}
+ \item Rechenwerk (ALU)
+ \item Speicher\pause: Register, adressierbarer Hauptspeicher
+ \pause
+ \item Takt\pause: Befehle abarbeiten
+ \pause
+ \item Peripherie: Kommunikation mit der Außenwelt
+ \pause
+ \arrowitem in Maschinensprache programmierbar
+ \end{itemize}
+
+\end{frame}
+
+\sectionnonumber{\inserttitle}
+
+\begin{frame}
+
+ \showsectionnonumber
+
+ \begin{itemize}
+ \item[\textbf{1}] \textbf{Einführung}
+ \item[\textbf{2}] \textbf{Vom Schaltkreis zum Computer}
+ \begin{itemize}
+ \item[2.1] Logik-Schaltkreise
+ \item[2.2] Binärdarstellung von Zahlen
+ \item[2.3] Vom Logik-Schaltkreis zum Addierer
+ \item[2.4] Negative Zahlen
+ \color{orange}
+ \item[2.5] Vom Addierer zum Computer
+ \item[\dots]
+ \end{itemize}
+ \color{gray}
+ \item[\textbf{3}] \textbf{Architekturmerkmale von Prozessoren}
+ \item[\textbf{4}] \textbf{Der CPU-Stack}
+% \item[\textbf{5}] \textbf{Hardwarenahe Programmierung}
+% \item[\textbf{6}] \textbf{Anwender-Software}
+% \item[\textbf{7}] \textbf{Bus-Systeme}
+% \item[\textbf{8}] \textbf{Pipelining}
+ \item[\textbf{\dots\hspace{-0.75em}}]
+% \item[\textbf{9}] \textbf{Ausblick}
+ \end{itemize}
+
+\end{frame}
+
+\end{document}