I'm making this guide to teach about boolean algebra and logic gates, and how to do stuff with it in nimbatus or anywhere else really.

Boolean algebra is a part of algebra where variables can only have the values true and false, usually represented by 1 and 0.
It uses logical operators like conjunction AND, disjunction OR and negation NOT instead of the arithmetic operators used in normal algebra.

The most basic "operator" is the Statement. It has an input and an output, the output is always equal to the input. In an ideal logic gate system, this wouldn't be very useful.
Though, because usually we don't have an ideal system, it has some uses.
In real world electronics, it allows for isolating the input from the output, with various types of Buffers such as the tri-state buffer allowing electrically separating input and output for certain states.
Additionally, in both real world electronics and most logic systems, logic gates don't work instantaneously, causing a buffer to buffer the value and add short delay.

• Y = A

The second most basic operator is the Negation. Like the buffer, it also has an input and an output, though here, the output is always the inverse of the input: if the input is true, the output is false.

• Y = A̅
  
• Y = NOT A
  
• Y = ¬A
  
• Y = Ã
  
• Y != A
  
• Y = Na

The Disjunction operator has two inputs and one output.
Disjunction can be thought of as a simple wire connecting together both inputs and the output, turning on the output if at least one input has the value true.

• Y = A OR B
  
• Y = A ∨ B
  
• Y = A + B
  
• Y = A ∪ B
  
• Y = A | B
  
• Y= Aab

The Conjunction operator, like the Disjunction operator, has two inputs and one output.
Its Output is true, if both inputs are true: for the inputs A, B the output is true if A AND B are true.

• Y = A AND B
  
• Y = A ∧ B
  
• Y = A ⋅ B
  
• Y = A B
  
• Y = A & B
  
• Y = A ∩ B
  
• Y = Kab

Other, secondary operators can be constructed from those basic operators, the most common being Exclusive Or (XOR) and Equivilancy (XNOR). Two other, rarely used operators are Implication (IMPLY) and Nonimplication (NIMPLY)
These can be composed from the three basic operators:
A→B = ¬A ∨ B (Implies)
A⊕B = (A ∨ B) ∧ ¬(A ∧ B) (XOR)
A≡B = ¬(A⊕B) (XNOR)

• Y = A XOR B
  
• Y = A⊕B
  
• Y = Jab

• Y = A→B
  
• Y = Cab
  
• Y = A Implies B

• Y = A XNOR B
  
• Y = A ≡ B
  
• Y = Eab

Boolean algebra uses truth tables to express the values of operations
For this part please refer to the wikipedia article:
Laws[en.wikipedia.org]

This Section is about Logic gates, logic gates are devices that implement a Boolean Function, it has binary inputs and outputs. I will not go into how they are built in the real world, I will mainly list the symbol set named "Distinctive Shape" (defined in IEEE Std 91/91a-1991 (left)) and the set named "Rectangular Shape" (defined in IEEE Std 91/91a-1991 IEC 60617-12 : 1997 (right)) for them.

Under Construction

EDIT: I am finally in the process of finishing this guide, until then, here is a really good ongoing video series about this topic https://www.youtube.com/playlist?list=PLFt_AvWsXl0dPhqVsKt1Ni_46ARyiCGSq


This guide is still being expanded. For now you can get the informations here:
https://en.wikipedia.org/wiki/Boolean_algebra
https://en.m.wikipedia.org/wiki/Logic_gate
https://en.wikipedia.org/wiki/Flip-flop_(electronics)
https://en.wikipedia.org/wiki/Adder_(electronics)
https://en.wikipedia.org/wiki/Binary_decoder
https://en.wikipedia.org/wiki/Multiplexer
And a program to design Logic circuits:
http://www.cburch.com/logisim/

"Live long and prosper" - George Boole