ece124: add base logic

docs/1b/ece124.md

@@ -65,6 +65,31 @@ $$
 
 Please see [ECE 108: Discrete Math 1#Operator laws](/1b/ece108/#operator-laws) for more information.
 
+AND and OR are commutative.
+
+- $x\cdot y=y\cdot x$
+- $x+y=y+x$
+
+AND and OR are associative.
+
+- $x\cdot(y\cdot z)=(x\cdot y)\cdot z)$
+- ...
+
+AND and OR are distributive with each other.
+
+- $x\cdot (y+z)=x\cdot y+z\cdot z$
+
+A term that depends on another term ORed together can be "absorbed".
+
+- $x+x\cdot y=x$
+- $x\cdot(x+y)=x$
+
+If a term being true also results in other ORed terms being true, it is redundant and can be eliminated via consensus.
+
+- $x\cdot y+y\cdot z+x'\cdot z=x\cdot y+x'\cdot z$
+  - if y and z are true, at least one of the other two terms must be true
+- $(x+y)\cdot (y+z)\cdot(x'+z)=(x+y)\cdot (x'+z)$
+
 The **synthesis** of an algebraic formula represents its implementation via logic gates. In this course, its total cost is the sum of all inputs to all gates and the number of gates, *excluding* initial inputs of "true" or an initial negation.
 
 In order to deduce an algebraic expression from a truth table, **OR** all of the rows in which the function returns true and simplify.