ece124: add postulates

docs/1b/ece124.md

@@ -45,3 +45,26 @@ The **NOT** operator returns the opposite of its singular input.
 $$\overline A \text{ or } A'$$
 
 <img src="https://upload.wikimedia.org/wikipedia/commons/6/60/NOT_ANSI_Labelled.svg" width=200>(Source: Wikimedia Commons)</img>
+
+### Postulates
+
+In binary algebra, if $x,y,z\in\mathbb B$ such that $\mathbb B=\{0, 1\}$:
+
+The **identity element** for **AND** $1$ is such that any $x\cdot 1 = x$.
+
+The **identity element** for **OR** $0$ is such that any $x + 0 = x$.
+
+In this space, it can be deduced that $x+x'=1$ and $x\cdot x'=0$.
+
+**De Morgan's laws** are much easier to express in boolean algebra, and denote distributing a negation by flipping the operator:
+
+$$
+(x\cdot y)'=x'+y' \\
+(x+y)=x'\cdot y'
+$$
+
+Please see [ECE 108: Discrete Math 1#Operator laws](/1b/ece108/#operator-laws) for more information.
+
+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.