Logic gates examples

1. Logic Gates
Unit III

2. EXERCISE
1. Evaluate the following Boolean expression using Truth
Table.
(a) X’Y’+X’Y (b) X’YZ’+XY’
(c) XY’(Z+YZ’)+Z’
2. Verify that P+(PQ)’ is a Tautology.
3. Verify that (X+Y)’=X’Y’

3. AND GATE
So while going out of the house you set the "Alarm
Switch" and if the burglar enters he will set the "Person switch",
and tada the alarm will ring.
PRACTICAL APPLICATIONS OF LOGIC GATES

4. AND GATE
PRACTICALAPPLICATIONS OF LOGIC GATES
Electronic door will only open if it detects a person and the
switch is set to unlocked.
Microwave will only start if the start button is pressed and
the door close switch is closed.

5. OR GATE
You would of course want your doorbell to ring
when someone presses either the front door switch or the
back door switch..(nice)
PRACTICALAPPLICATIONS OF LOGIC GATES

6. NOT GATE
When the temperature falls below 20c the Not gate will
set on the central heating system (cool huh).
PRACTICAL APPLICATIONS OF LOGIC GATES

7. XOR GATE
 XOR, or exclusive OR, gate
 An XOR gate produces 0 if its two inputs are the same,
and a 1 otherwise
 Note the difference between the XOR gate
and the OR gate; they differ only in one
input situation
 When both input signals are 1, the OR gate produces a 1
and the XOR produces a 0

8. XOR GATE

9. NAND AND NOR GATES
 The NAND and NOR gates are essentially the opposite of the AND
and OR gates, respectively
 Known as a “universal” gate because ANY digital circuit can be
implemented with NAND & NOR gates alone.

10. NAND GATE
X
X
F = (X•X)’
= X’+X’
= X’
X
Y
Y
F = ((X•Y)’)’
= (X’+Y’)’
= X’’•Y’’
= X•Y
F = (X’•Y’)’
= X’’+Y’’
= X+Y
X
X
F = X’
X
Y
Y
F X•Y
F = X+Y

11. NOR GATE
NOR
X
Y
Z
X Y Z
0 0 1
0 1 0
1 0 0
1 1 0
Z = ~(X | Y)
nor(Z,X,Y)

12. EXCLUSIVE-OR GATE
X Y Z
XOR
X
Y
Z 0 0 0
0 1 1
1 0 1
1 1 0
Z = X ^ Y
xor(Z,X,Y)

13. EXCLUSIVE-NOR GATE
X Y Z
XNOR
X
Y Z 0 0 1
0 1 0
1 0 0
1 1 1
Z = ~(X ^ Y)
Z = X ~^ Y
xnor(Z,X,Y)

14. GATES WITH MORE INPUTS
 Gates can be designed to accept three or more input values
 A three-input AND gate, for example, produces an output of 1
only if all input values are 1

15. CIRCUITS
 Two general categories
 In a combinational circuit, the input values explicitly
determine the output
 In a sequential circuit, the output is a function of the input
values as well as the existing state of the circuit
 As with gates, we can describe the operations
of entire circuits using three notations
 Boolean expressions
 logic diagrams
 truth tables

16. COMBINATIONAL CIRCUITS
 Gates are combined into circuits by using the output of one gate
as the input for another

17. COMBINATIONAL CIRCUITS
 Because there are three inputs to this circuit, eight rows are
required to describe all possible input combinations
 This same circuit using Boolean algebra:
(AB + AC)

18. NOW LET’S GO THE OTHER WAY; LET’S
TAKE A BOOLEAN EXPRESSION AND DRAW
 Consider the following Boolean expression: A(B + C)
• Now compare the final result column in this truth table to the
truth table for the previous example
• They are identical

19. PROPERTIES OF BOOLEAN ALGEBRA

20. ADDERS
 At the digital logic level, addition is performed in binary
 Addition operations are carried out
by special circuits called, appropriately, adders
 The result of adding two binary digits could produce a carry
value
 Recall that 1 + 1 = 10
in base two
 A circuit that computes the sum of two bits
and produces the correct carry bit is called a half adder

21. ADDERS
 Circuit diagram representing
a half adder
 Two Boolean expressions:
sum = A  B
carry = AB

22. BASIC THEOREM OF BOOLEAN ALGEBRA
T1 : Properties of 0
(a) 0 + A = A
(b) 0 A = 0
T2 : Properties of 1
(a) 1 + A = 1
(b) 1 A = A
T3 : Commutative Law
(b) A + B = B + A
(b) A B = B A
T4 : Associate Law
(a) (A + B) + C = A + (B + C)
(b) (A B) C = A (B C)

23. BASIC THEOREM OF BOOLEAN ALGEBRA
T5 : Distributive Law
(a) A (B + C) = A B + A C
(b) A + (B C) = (A + B) (A +
C)
(c) A+A’B = A+B
T6 : Indempotence (Identity ) Law
(a) A + A = A
(b) A A = A
T7 : Absorption (Redundance) Law
(a) A + A B = A
(b) A (A + B) = A

24. T8 : Complementary Law
(a) X+X’=1
(b) X.X’=0
T9 : Involution
(a) x’’ = x
T10 : De Morgan's Theorem
(a) (X+Y)’=X’.Y’
(b) (X.Y)’=X’+Y’
BASIC THEOREM OF BOOLEAN ALGEBRA

25. DE MORGAN'S THEOREM 1
Theorem 1 A . B = A + B

26. DE MORGAN'S THEOREM 1
Theorem 1 A . B = A + B

27. DE MORGAN'S THEOREM 1
Theorem 1 A . B = A + B

28. DE MORGAN'S THEOREM 2
Theorem 1 A + B = A . B

29. DE MORGAN'S THEOREM 2
Theorem 2 A + B = A . B

30. DE MORGAN'S THEOREM 2
Theorem 2 A + B = A . B

31. Thank You