Logical Gates

1. Gates
Gates are Fundamentals Building blocks of digital system.
These are digital circuits constructed from diodes, transistors and resistors
that produce output from some given inputs. They are also called Logic
Gates. Tables of Gates called “Truth Tables”.
In Logic Gates, we use binary values (1, 0). We can say Low and High
values (1=high value, 0=low value). We have other names of these values,
are True and False (1=true, 0=false). Usually Gates have two inputs except
the NOT gate.
We have 7 gates. AND, OR, NOT, NOR, NAND, XOR and XNOR.
(1) AND:
In AND gate, if we have both inputs true, then output
will be true. Otherwise the output will be false.
Operation: A.B & A&B
(2) OR:
In OR gate, if any input is true then output
Will be true.
Operation: A+B
Input Output
A B A AND B
0 0 0
0 1 0
1 0 0
1 1 1
Input Output
A B A OR B
0 0 0
0 1 1
1 0 1
1 1 1
Truth Table

2. (3) NOT:
This gate has only one input. We also called it
Inverter. It inverts the values.
Operation: or ~
(4) NAND:
It is addition of AND gate with NOT gate,
they form NAND gate. NOT gate inverted
outputs of AND gate and give the result of
a NAND gate.
Operation: A.B or A|B
(5) NOR:
It is addition of OR and NOT gate.
The small ball ( ) indicates NOT gate.
Operation: A+B or A-B
Input Output
A NOT A
1 0
0 1
Input Output
A B A NAND B
0 0 1
0 1 1
1 0 1
1 1 0
Input Output
A B A NOR B
0 0 1
0 1 0
1 0 0
1 1 0

3. (6) XOR:
In XOR gate, same inputs give False
output, and different inputs give True
output.
Operation:
(7) XNOR:
It is addition of XOR and NOT gates. We
simply read it “ex-nor” or “e-nor”.
Basically, it is “exclusive-NOR”.
Operation: or
Using combinations of logic gates, complex operations can be
performed.In theory, there is no limit to the number of gates that can be
arrayed together in a single device. But in practice, there is a limit to the
number of gates that can be packed into a given physical space.
Input Output
A B A XOR B
0 0 0
0 1 1
1 0 1
1 1 0
Input Output
A B A XNOR B
0 0 1
1 0 0
0 1 0
1 1 1