Added Derived Gates and Modified basic gates along with explanation, symbols, examples and Truth Tables.

boolean_algebra/README.md

@@ -2,6 +2,128 @@
 
 Boolean algebra is used to do arithmetic with bits of values True (1) or False (0).
 There are three basic operations: 'and', 'or' and 'not'.
+Special or derived operations are : 'NAND', 'NOR', 'XOR' and 'XNOR'
+
+AND :
+The AND operation in Boolean algebra gives a result of 1 (True) only when all the input variables are 1 (True).
+If any input is 0 (False), the output will be 0 (False).
+
+Symbol: · or ∧
+Example: If A = “I study” and B = “I sleep early”,
+then A AND B means “I study and I sleep early”.
+------------------------------
+    |INPUT A  | INPUT B | Output |
+    ------------------------------
+    |    0    |    0    |    0   |
+    |    0    |    1    |    0   |
+    |    1    |    0    |    0   |
+    |    1    |    1    |    1   |
+    ------------------------------
+
+OR :
+The OR operation gives a result of 1 (True) when at least one of the input variables is 1 (True).
+It gives 0 (False) only when all inputs are 0 (False).
+
+Symbol: + or ∨
+Example : If A = “I study” and B = “I sleep early”,
+then A OR B means “I study or I sleep early”.
+
+ ------------------------------
+    | INPUT A | INPUT B | Output |
+    ------------------------------
+    |    0    |    0    |    0   |
+    |    0    |    1    |    1   |
+    |    1    |    0    |    1   |
+    |    1    |    1    |    1   |
+    ------------------------------
+
+NOT:
+The NOT operation is a unary operation (works on one variable).
+It inverts the value of the variable —
+if the input is 1 (True), the output becomes 0 (False), and vice versa.
+
+Symbol: Overline ( ̅ ), ¬, or !
+Example : If A = “It’s raining”, then NOT A means “It’s not raining”.
+
+ ------------------------------
+    |    A    |    A̅    |
+    ------------------------------
+    |    0    |    1    |
+    |    1    |    0    |
+    ------------------------------
+
+NAND:
+The NAND operation is the inverse of the AND operation.
+It gives an output of 0 (False) only when all inputs are 1 (True).
+For all other combinations, the output is 1 (True).
+
+Symbol: (A · B)̅ or ¬(A ∧ B)
+Example:
+If A = “I study” and B = “I sleep early”,
+then A NAND B means “It’s not true that I study and sleep early both.”
+
+
+------------------------------
+    | INPUT A | INPUT B | Output |
+    ------------------------------
+    |    0    |    0    |    1   |
+    |    0    |    1    |    1   |
+    |    1    |    0    |    1   |
+    |    1    |    1    |    0   |
+    ------------------------------
+
+NOR:
+The NOR operation is the inverse of the OR operation.
+It gives an output of 1 (True) only when all inputs are 0 (False).
+If any input is 1 (True), the output becomes 0.
+
+Symbol: (A + B)̅ or ¬(A ∨ B)
+Example : If A = “I study” and B = “I sleep early”,
+then A NOR B means “Neither I study nor I sleep early.”
+
+------------------------------
+    | INPUT A | INPUT B | Output |
+    ------------------------------
+    |    0    |    0    |    1   |
+    |    0    |    1    |    0   |
+    |    1    |    0    |    0   |
+    |    1    |    1    |    0   |
+    ------------------------------
+
+XOR:
+The XOR (Exclusive OR) operation gives an output of 1 (True) only when exactly one of the inputs is 1 (True).
+If both inputs are the same (both 0 or both 1), the output is 0 (False).
+
+Symbol: ⊕ or A XOR B
+Example:
+If A = “I study” and B = “I sleep early”,
+then A XOR B means “I study or I sleep early, but not both.”
+
+------------------------------
+    | INPUT A | INPUT B | Output |
+    ------------------------------
+    |    0    |    0    |    0   |
+    |    0    |    1    |    1   |
+    |    1    |    0    |    1   |
+    |    1    |    1    |    0   |
+    ------------------------------
+
+XNOR:
+The XNOR (Exclusive NOR) operation is the inverse of the XOR operation.
+It gives an output of 1 (True) when both inputs are the same — either both 0 or both 1.
+If the inputs are different, the output is 0 (False).
+
+Symbol: ⊙ or (A ⊕ B)̅ or A XNOR B
+Example: If A = “I study” and B = “I sleep early”,
+then A XNOR B means “Either I study and sleep early both, or neither I study nor sleep early.”
+------------------------------
+    | INPUT A | INPUT B | Output |
+    ------------------------------
+    |    0    |    0    |    1   |
+    |    0    |    1    |    0   |
+    |    1    |    0    |    0   |
+    |    1    |    1    |    1   |
+    ------------------------------
 
 * <https://en.wikipedia.org/wiki/Boolean_algebra>
 * <https://plato.stanford.edu/entries/boolalg-math/>