Logic Gate

Definition of Logic Gate

•  A logic gate is an idealized or physical device implementing a Boolean function. Logic gates perform basic logical functions and are the are the fundamental building blocks of digital integrated circuits. Most logic gates take an input of two binary values, and output a single value of a 1 or 0. Some circuits may have only a few logic gates, while others, such as microprocessors, may have millions of them. There are seven different types of logic gates, which are outlined below. 

•  In the following examples, each logic gate except the NOT gate has two inputs, A and B, which can either be 1 (True) or 0 (False). The resulting output is a single value of 1 if the result is true, or 0 if the result is false.

1.  AND - True if A and B are both True

2.  OR - True if either A or B are True

3.  NOT - Inverts value: True if input is False; False if input is True

4.  XOR - True if either A or B are True, but False if both are True

5.  NAND - AND followed by NOT: False only if A and B are both True

6.  NOR - OR followed by NOT: True only if A and B are both False

7.  XNOR - XOR followed by NOT: True if A and B are both True or both False

THE AND GATE
ØAn AND gate is a logic circuit that performs the AND

   operation on the circuit’s inputs.
Ø The AND gate operation is performed by multiplication of 1s and 0s.
ØThe Boolean expression for AND operation is :

                Output = A . B
Ø If 0  is called “false” and 1 is called “true”, an output of
   AND gate will only get 1 if both input of AND gate is 1.
   Otherwise, the output will be always 0 .

AND gate

Input A	Input B	Output
	1
1
1	1	1

THE OR GATE
ØAn OR gate is a logic circuit that performs an OR operation on the circuit’s input.
Ø  The output is "true" if either or both of the inputs are "true." If both inputs are "false," then the output is "false."
Ø  The Boolean expression for OR operation is :
                              Output = A + B

         

                           OR gate

Input A	Input B	Output
	1	1
1		1
1	1	1

THE NOT GATE

Ø A logical inverter , sometimes called a NOT gate to differentiate it from other types of electronic inverter devices, has only one input. It reverses the logic state.

                                         

THE NAND GATE
ØThe NAND gate is a combination of NOT - AND.

ØIt acts in the manner of the logical operation " and " followed by a negation. The output is "false" if both inputs are "true".
    Otherwise the outputs is "true"

ØThe Boolean expression of NAND  operation is :
                                    Output = A' . B'

                                                 NAND gate

Input A	Input B	Output
		1
	1	1
1		1
1	1

THE NOR GATE
ØThe NOR gate is a combination OR gate followed by an inverter. Its outputs is "true" if both inputs are "false". Otherwise , the outputs is "false"

ØThe Boolean expression of NOR operation is :
                                Output = A' + B'

NOR gate

Input A	Input B	Output
		1
	1
1
1	1

THE EXCLUSIVE-OR / XOR GATE

ØThe Boolean expression of XOR operation is :

                               Output = A . B' + A' . B

                                         XOR gate

Input 1	Input 2	Output
	1	1
1		1
1	1

THE EXCLUSIVE-NOR / XNOR GATE

ØThe XNOR (exclusive-NOR) gate is a combination XOR gate
   
    followed by an inverter. Its output is "true" if the inputs are the 
     
     same, and "false" if the inputs are different .

XNOR gate

Input A	Input B	Output
		1
	1
1
1	1	1

                               Written by EOH WENG JIAN (B031210151)