Basic Gates (AND, OR, NOT) Universal Gates (NAND, NOR) EX-OR, EX-NOR

1. LOGIC GATES:
Logic gates are the basic building blocks of any digital system. It is an electronic circuit
having one or more than one input and only one output.
The relationship between i/p & o/p is based on certain logic.
LOGIC GATES
Basic Logic Gate Universal Logic Gate
Ex-OR EX-NOR
AND OR NOT NAND NOR
Any Logical gate → (Name, Definition, Symbol, Boolean Expression, Truth Table)
1. AND Gate:
It consists 2 or more than 2 i/p lines & 1 o/p line. It provides high o/p when only all i/p(s)
are high and in rest condition it will provides low o/p.
Digital having 2 values (0, 1) (1 → high, 0 → low)
(10*20999*10798787634794389*0 = 0)
Logical symbol of AND Gate:
Y = A AND B = A . B (read as A dot B, A & B)
Y = A AND B AND C………..upto n terms = A . B . C . upto n terms
Y = A.B
Truth Table: It is a tabular representation which will show the relation between i/p &
o/p. It tells how o/p is varying a/c to the i/p.
Truth Table for AND Gate:
Inputs Output
A B Y
0 0 0
0 1 0
1 0 0

2. 1 1 1
1.1.1.1..1.1.1.1..1…………1…………….1 = 1
2. OR GATE:
It consists 2 or more than 2 i/p lines & 1 o/p line. It provides low o/p when only all i/p(s)
are low and in rest condition it will provides high o/p.
Y = A OR B = A+B (OR → +)
Y = A OR B OR C OR up to n terms ( A+B+C+ up to n terms)
Inputs Output
A B Y
0 0 0
0 1 1
1 0 1
1 1 1
Y = A+B+C+D……………up to 100 terms
3. NOT GATE: (Inverter) (Complement)
It consists 1 i/p line & 1 o/p line. It provides low o/p when i/p is high & vice versa.
Y = A’ = NOT (A) = A
I/P (A) O/P (B)
0 1
1 0

3. 4. NAND GATE: (NOT + AND)
Reverse of AND GATE, Compliment of AND GATE, Inverted AND GATE
Y = A AND B = A NAND B = A NOT AND B = A.B = (A.B)’
Truth Table of NAND GATE:
Inputs AND Output NAND O/P
A B Y1 Y
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0
NAND: It consists 2 or more than 2 i/p lines & 1 o/p line. It provides low o/p when only
all i/p(s) are high and in rest condition it will provides low o/p.
5. NOR GATES: (NOT + OR)
Reverse of OR GATE, Compliment of OR GATE, Inverted OR GATE

4. Inputs Intermediate
Output
Output
A B Y1 = A+B Y = (A+B)’
0 0 0 1
0 1 1 0
1 0 1 0
1 1 1 0
NOR: It consists 2 or more than 2 i/p lines & 1 o/p line. It provides high o/p when only all
i/p(s) are low and in rest condition it will provides low o/p.

5. EX-OR Gate (XOR Gate): Special type of gate, used for adder & subtractor. Exclusive -
OR Gate/X-OR Gate. It consists 2 or more than 2 i/p lines & 1 o/p line. It provides high
o/p, when only all inputs are different.
Y = A XOR B
Y = A’B + AB’
Inputs Output
A B Y
0 0 0
0 1 1
1 0 1
1 1 0
EX-NOR Gate (XNOR Gate): Special type of gate, used for adder & subtractor. Exclusive
N-OR Gate/X-NOR Gate. It consists 2 or more than 2 i/p lines & 1 o/p line. It provides
high o/p, when only all inputs are same.
Inputs Output
A B Y
0 0 1
0 1 0
1 0 0
1 1 1

7. AND → Y = A.B NAND → Y = (A.B)’
OR → Y= A+B N OR → Y = (A+B)’
NOT → Y = A’ Buffer → Y = A
XOR → Y = A ⊕ B XNOR → Y = (A ⊕ B)’
Q. What is Logic Gates? Classify & explain with their symbols, Boolean equations & truth
table.
Q. Why NAND & NOR Gates are called Universal Gates?
NAND & NOR Gates are called Universal Gates because Combinations of NAND/NOR can
be used to work as of the basic gates (AND, OR & NOT).
a) NAND Gate as a NOT Gate:
A a b Y
0 0 0 1
1 1 1 0
b) NAND as an AND Gate

8. (NAND = AND+NOT) → (AND = NAND - NOT)
(NAND = NOT + AND)
(AND = NAND + NOT)
A B Y1 Y
0 0 1 0
0 1 1 0
1 0 1 0
1 1 0 1
c) NAND as an OR Gate
A B Y1 Y2 Y
0 0
0 1
1 0
1 1
NAND → NOT (1 NAND gate required)

9. NAND → AND (2 NAND gates required)
NAND → OR (3 NAND gates required)
a) NOR as a NOT Gate
A a b Y
0 0 0 1
1 1 1 0
b) NOR as an OR Gate
A B Y1 Y
0 0 1 0
0 1 0 1
1 0 0 1
1 1 0 1
c) NOR as an AND Gate
A B Y1 Y2 Y
0 0 1 1 0
0 1 1 0 0
1 0 0 1 0
1 1 0 0 1