this presentation explains how data is represented in digital computer. it describes digital logic, logic gates and boolean functions. you can learn how to convert boolean function into logic circuit

2. COMPUTER LOGIC AND
GATES
Presenter: SAMINA KHAN
Fazaia Degree College Risalpur

3. DATA REPRESENTATION IN
COMPUTER
• Computer is an electronic machine
• It consists of millions of electronic
switches .
• If electronic switch is closed
electricity flows
• If electronic switch is open electricity
does not flows

4. DATA REPRESENTATION IN COMPUTER
• Switch has two states.
• when electronic switch is closed electricity
flows it is called 1 .
• when electronic switch is open electricity does
not flows it is called 0 .
• Therefore 0 and 1 are used in computer to
represent the two states of switch

6. How do computer represent data?
• Look at your keyboard
• It has many keys such as alphabet keys, number
keys and special keys.
• Whenever we type something using these keys,
computer represent that data in 1s and 0s
pattern.

8. How do computer represent data?
• These 1s and 0s are called bits.
• Bit is the abbreviation of binary digit.
• Humans understand words and pictures,
computer understand the binary pattern.

9. How the computer understand
the pattern of 1s and 0s?

10. • Computer detects the flow of current.
• 1 represents that the current flow in circuit
• 0 represent that the current is not flowing.

12. DIGITAL LOGIC & LOGIC
GATES

13. DIGITAL LOGIC
• It is fundamental in creating electronic devices
such as calculator, computer, digital watches
etc
• DIGITAL logic is used to create digital circuits
which consists of large number of logic gates

14. LOGIC GATES
• Logic gates are building blocks of digital
circuits used in computer and many other
devices .
• They have two or more inputs (high or low)
and produce a single output (high or low).

15. TRUTH TABLE
• The truth table represents a digital logic circuit
in table form.
• It shows how a logic circuit’s output responds
to all the possible combinations of the inputs
using logic “1” for True and logic “0” for False.

16. BASIC LOGIC GATES
• There are three basic logic gates:
• AND GATE
• OR GATE
• NOT GATE

17. AND GATE
• The AND gate has two or more inputs that can
be low (0) or high (1).
• The output is high when all the inputs are high.
• It produces low output only when at least one
of the inputs are low .

18. TRUTH TABLE FOR AND GATE
• The truth table for AND gate for two variables.

20. OR GATE
• An OR gate is a logic gate that performs logical
OR operation.
• A logical OR operation has a high output (1) if
one or both the inputs to the gate are high (1).
• If neither input is high, a low output (0)
results.

21. TRUTH TABLE FOR OR GATE
• The truth table of a 2 input OR gate can be
represented as:

23. NOT GATE
• Logic NOT gates provide the complement of
their input signal.
• When their input signal is “HIGH” their
output state will NOT be “HIGH”.
• When their input signal is “LOW” their output
state will NOT be “LOW”.

24. TRUTH TABLE FOR NOT GATE
• The truth table for NOT gate .
• The “bubble” (o) present at the end of
the NOT gate symbol above denotes a signal
inversion (complementation) of the output
signal.
1 0
0 1

26. NAND GATE
• The NAND gate is a combination of an
AND gate and NOT gate.
• It produces low output only when all inputs
are high .

27. TRUTH TABLE FOR NAND GATE
• The truth table for NAND gate for two
variables.
X Y AND
(A.B)
NAND
(A.B)
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0

29. NOR GATE
• The NOR gate combines the OR gate and NOT
gate.
• It is the result of the negation of the OR
operator.
• It produces low output only when any input is
high .
• A HIGH output (1) results if both the inputs to
the gate are LOW (0).

30. TRUTH TABLE FOR NOR GATE
• The truth table for NOR gate for two variables.
• The bubble indicates that the function of the
or gate has been inverted.

33. CREATING NAND AND NOR GATE
USING BASIC GATES

34. Creating NAND gate using AND
and NOT gates
• The NAND gate can be easily created by using
an AND gate and NOT gate.
• It is also called Negated And gate.

35. Creating NOR gate using OR and
NOT gates
• The NOR gate can be created by using OR and
NOT gate.

36. Exclusive OR GATE(XOR gate)
• An XOR gate implements an exclusive or; that
is, a true output results if one, and only one,
of the inputs to the gate is true. If both inputs
are false or both are true, a false output
results.

37. Exclusive OR GATE(XOR gate)
• It is a type of logic gate use to perform a
Boolean expression: F= X.Y+X.Y
• To perform this Boolean function we need
three different logic gates.
oNOT gate (to find NOT of X & Y)
oAND gate (to find X.Y & X.Y)
oOR gate ( to perform addition operation
X.Y+X.Y

38. TRUTH TABLE FOR Exclusive OR
GATE(XOR gate)
X Y
0 0
0 1
1 0
1 1
X Y
1 1
1 0
0 1
0 0
XY
0
1
0
0
XY
0
0
1
0
F= X.Y+X.Y
F
0
1
1
0

39. SYMBOL FOR Exclusive OR
GATE(XOR gate)

40. HOW Exclusive OR GATE WORK?

41. Exclusive NOR GATE(XNOR gate)
• The XNOR gate is the complement of the XOR
gate

42. TRUTH TABLE FOR Exclusive NOR
GATE(XNOR gate)
X Y
0 0
0 1
1 0
1 1
F= X.Y+X.Y
XNOR
1
0
0
1
XOR
0
1
1
0

43. SYMBOL FOR Exclusive NOR
GATE(XNOR gate)

44. References
• https://www.electronics-tutorials.ws/logic/logic_4.html
• https://www.vivaxsolutions.com/physics/allogicgates.aspx
• https://www.tutorialspoint.com/computer_logical_organization/logic_gates.htm
• https://techterms.com/definition/logicgate
• https://whatis.techtarget.com/definition/logic-gate-AND-OR-XOR-NOT-NAND-NOR-and-
XNOR