Definition:
Logic gates are building blocks for
building Digital circuits.
1.
AND GATE :
AND gate show the output
true if both input terminal respectively a and
b are at 1,otherwise its output is
zero .
Boolian expression:
NOTE: HERE X SHOWS THE OUTPUT.
X=A.B
Truth
Table:
X=A.B
|
A
|
B
|
X
|
|
0
|
1
|
0
|
|
1
|
0
|
0
|
|
1
|
1
|
1
|
|
0
|
0
|
0
|
2.
Or gate :
Output will be true if
one of the terminals is at 1,zero only if both terminals are at 0.
Boolian Expression:
X=A+B
Truth table:
|
A
|
B
|
X
|
|
1
|
0
|
1
|
|
1
|
1
|
1
|
|
0
|
1
|
1
|
|
0
|
0
|
0
|
3.
NOT Gate
Not gate invert the
actual output of gate, if a terminal is at 1 output will be zero.
Boolian Expression
X=
Truth Table:
|
A
|
X
|
|
1
|
0
|
|
0
|
1
|
Where X is output.
4.
NAND GATE:
This gate is the
combination of NOT and AND gates.
It inverts the actual
output of AND gate.
Boolian Expression:
Truth Table:
|
X
|
A
|
B
|
|
0
|
1
|
1
|
|
1
|
0
|
1
|
|
1
|
0
|
0
|
|
|
|
|
|
|
|
|
5.
NOR GATE:
This gate is the
combination of NOT and OR
it inverts the actual output of OR gate so if terminal a is at 1 and
b is at 0 the output will be 0.
Boolian Expression:
Truth Table:
|
X
|
A
|
B
|
|
0
|
1
|
0
|
|
1
|
O
|
O
|
|
0
|
1
|
1
|
6.
EXOR GATE:
The Exclusive -OR gate. True if either A or B are
True, but False if both are True.
Boolian Expression:
Truth Table:
|
X
|
A
|
B
|
|
0
|
0
|
0
|
|
0
|
1
|
1
|
|
1
|
1
|
0
|
|
1
|
0
|
1
|
|
|
|
|
7.
XNOR GATE:
This gate is obtained
simply by inverting the output of XOR.
Boolian Expression:
Truth Table:
|
X
|
A
|
B
|
|
1
|
0
|
0
|
|
1
|
1
|
1
|
|
0
|
1
|
0
|
|
0
|
0
|
1
|
Conversion Of Binery Numbers
8.
Conversion from Binary to Decimal
Examples:
101012
= 1×24+0×23+1×22+0×21+1×20 =
16+4+1= 21
101112 =
1×24+0×23+1×22+1×21+1×20 =
16+4+2+1= 23
9.
Conversion of Octal numbers to
Decimal
Examples:
278 =
2×81+7×80 = 16+7 = 23
308 =
3×81+0×80 = 24
43078 =
4×83+3×82+0×81+7×80= 2247
10.
Conversion of Hexadecimal To Decimal
Examples:
2816 =
28H = 2×161+8×160 = 40
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