Lectures

https://www.allaboutcircuits.com/textbook/digital/chpt-7/circuit-simplification-examples/


Truth Tables and symbols

    Using truth tables to represent input and output of a gate
       NOT

       AND/NAND

       OR/NOR

       XOR/XNOR



More complex circuits.
  OR from 4 NANDs   !(!(A*A)*!(B*B)) = A+B



A  B
 |
A*A
|
!(A*A)
|
B*B
|
!(B*B)
|
!(A*A) * !(B*B)
|
!( !(A*A) * !(B*B))

-----
+
-----
+
-------
+
-----
+
--------
+
----------------
+
--------------------

0  0
|
0
|
1
|
0
|
1
|
1
|
0

0  1
|
0
|
1
|
1
|
0
|
0
|
1

1  0
|
1
|
0
|
0
|
1
|
0
|
1

1  1
|
1
|
0
|
1
|
0
|
0
|
1



       AND from NORs  !(!(A+A) + !(B+B)) = A*B

       XOR   !(A*B)*(A+B)

   Both logically and with physical electronic, it is often easier to 
     work with the inverted version of a logic gate.
 
AND from NORs  !(!(A+A)+!(B+B)) = A*B
  

    
!(!(A+A)+!(B+B)) = !(!A+!B)
Idempotent
    
!(!A+!B) = !(!(A*B))         
DeMorgan
    
!!(A*B)  = A*B               
Cancellation