Revisiting the Axioms of Boolean Algebra

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What is an axiom?
An axiom is a fundamental truth or assumption accepted without proof.

What are the AND axioms?
The AND axioms are:

  • .
  • .
  • .

What are the OR axioms?
The OR axioms are:

  • .
  • .
  • .

What are the NOT axioms?
The NOT axioms are:

  • If , then .
  • If , then .

What is a theorem?
A theorem is a statement proven to be true using axioms.

What are the fundamental theorems of Boolean algebra? (1)
The fundamental theorems of Boolean algebra are:

Laws / Theorems
Boundness law
Identity law
Idempotent theorem
Involution theorem
Complement law
Commutative law
Associative law
Distributive law
DeMorgan's law (1)
Absorption law
Consensus theorem
Note

Two variables right next to each other means AND:

Inverted Logic

What are the three inverted logic gates?
The three inverted logic gates are:

  1. NAND = AND + NOT.
  2. NOR = OR + NOT.
  3. XNOR () = XOR + NOT.

What is inverted with inverted logic gates?
With inverted logic gates, their output is inverted.

What are the three compound symbols for NAND, NOR, and XNOR?
The three compound symbols for NAND, NOR, and XNOR are:
NAND, NOR, and XNOR.png

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The De Morgan's Law

According to DeMorgan's law, what is the negation of AND equal to?
According to DeMorgan's law, the negation of AND is equal to NOT OR NOT .

According to DeMorgan's law, what is the negation of A OR B equal to?
According to DeMorgan's law, the negation of OR is equal to NOT AND NOT .

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Part 2: Intro to Verilog HDL

What does HDL stand for?
HDL stands for Hardware Descriptive Language.

What is the syntax for a logic gate in Verilog HDL?
The syntax for a logic gate in Verilog HDL is gate_name(out_ports, in_ports).

What is a module in Verilog HDL?
In Verilog HDL, a module is a container for a logic circuit with input and output ports, and a custom name.

Example
module riverfront(x, y, q);
	input x, y;
	output q;
	and(q, x, y);
endmodule