The logic gates have one or many input and only one output.The gates used to form integrated circuits (IC's) for digital circuit with combination and sequential of gates.this gates are of mainly 6 types .The three are basic gates and others are the prepared from basic gates called as derived gates.They are as follow:-
I ) Basic gates :-
i ) OR gate
ii) AND gate
iii)NOT gate
II) Derived gates :-
i ) NOR gate
ii) NAND gate
iii)EX-OR gate
The Logic gates have the following details:
1)Logic:-It is the statement.
2)Truth table:-It shows the input provided and output get.It is combination of input provided making rows in the table with inputs and output column.
3)Boolean equation :-It is the mathematical representation with the equation.
4)Symbol:-It is the logical symbol of the logic gate.
1) OR gate
Logic :- If A is true or B is true then Y is true
Boolean Equation :- Y=A+B
Truth table:
Symbol:-
2) AND gate
Logic :- If A is true and B is true then Y is true
Boolean Equation :- Y=A.B or Y=AB
Truth table:
Symbol:-
3) NOT gate
Logic :- If A is true then Y is false and A is false then Y is true
Boolean Equation :- Y=A.B or Y=AB
Truth table:
Symbol :-
4) NAND gate
Truth table:
Boolean Equation :- Y=A.B
Symbol:-
5) NOR gate
Boolean Equation :- Y=A+B
Truth table:
Symbol :-
6)EX-OR gate:
Y=A.B+A.B
Logic :When A is true or Bis true but not both then Y is true.
Truth table:
Symbol :-
De Morgan's Law :-
First law :-
Statement:-The compliment of sum is equal to product of compliments.
Boolean Equation :- A+B = A.B
Second Law :-
Statement:-The compliment of product is equal to sum of compliments.
Boolean Equation :- A.B = A+B
Half Adder:-
For addition of two bits half adder is used .
Truth table:
From the above table we can conclude that gates used in half adder are AND gate for carry and EX-OR gate for Sum.
I ) Basic gates :-
i ) OR gate
ii) AND gate
iii)NOT gate
II) Derived gates :-
i ) NOR gate
ii) NAND gate
iii)EX-OR gate
The Logic gates have the following details:
1)Logic:-It is the statement.
2)Truth table:-It shows the input provided and output get.It is combination of input provided making rows in the table with inputs and output column.
3)Boolean equation :-It is the mathematical representation with the equation.
4)Symbol:-It is the logical symbol of the logic gate.
1) OR gate
Logic :- If A is true or B is true then Y is true
Boolean Equation :- Y=A+B
Truth table:
| A | B | Y |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
Symbol:-
2) AND gate
Logic :- If A is true and B is true then Y is true
Boolean Equation :- Y=A.B or Y=AB
Truth table:
| A | B | Y |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Symbol:-
3) NOT gate
Logic :- If A is true then Y is false and A is false then Y is true
Boolean Equation :- Y=A.B or Y=AB
Truth table:
| A | Y |
| 0 | 1 |
| 1 | 0 |
Symbol :-
Truth table:
| A | B | Y |
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Boolean Equation :- Y=A.B
Symbol:-
Boolean Equation :- Y=A+B
Truth table:
| A | B | Y |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
Symbol :-
6)EX-OR gate:
Y=A.B+A.B
Logic :When A is true or Bis true but not both then Y is true.
Truth table:
| A | B | Y |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Symbol :-
De Morgan's Law :-
First law :-
Statement:-The compliment of sum is equal to product of compliments.
OR
The NOR gate is equivalent to bubbled NAND gate.Boolean Equation :- A+B = A.B
Second Law :-
Statement:-The compliment of product is equal to sum of compliments.
OR
The NAND gate is equivalent to bubbled OR gate.Boolean Equation :- A.B = A+B
Half Adder:-
For addition of two bits half adder is used .
Truth table:
| A | B | Carry | SUM |
| 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 |
From the above table we can conclude that gates used in half adder are AND gate for carry and EX-OR gate for Sum.
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