From b7693c4b70ba2514d9007891b267f1876473258e Mon Sep 17 00:00:00 2001
From: Julian T <julian@jtle.dk>
Date: Sun, 7 Feb 2021 21:44:39 +0100
Subject: Opgaver til digitalt design

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 sem6/dig/mm1/opgaver.md | 54 +++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 54 insertions(+)
 create mode 100644 sem6/dig/mm1/opgaver.md

diff --git a/sem6/dig/mm1/opgaver.md b/sem6/dig/mm1/opgaver.md
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+# Opgave 1
+
+Nope
+
+# Opgave 2
+
+    Show that the following
+
+    R = ~(~(A * ~B) * ~(~A * B))
+
+    is XOR
+
+Man kan skrive exclusive or som:
+
+```
+(A + B) * ~(A * B)
+
+(A + B) * (~A + ~B)
+A * ~A + A * ~B + B * ~A + B * ~B
+A * ~B + B * ~A
+~(~(A * ~B) * ~(~A * B))
+```
+
+yaay
+
+# Opgave 3
+
+    Reduce the following
+
+Jeg tager bare den først.
+
+```
+A * ~B * ~C + A * B * ~C + ~A * ~C
+
+~C * (A * ~B + A * B) + ~A * ~C
+~C * A + ~A * ~C
+~C
+```
+
+# Opgave 4
+
+    Find expression
+
+```
+X = ~(A * B)
+Y = ~(A * X)
+Z = ~(B * X)
+C = ~(Y * Z)
+D = ~X
+
+C = ~(~(A * ~(A * B)) * ~(B * ~(A * B)))
+D = ~~(A * B) = A * B
+```
+
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