I made these slides for the presentation of one of my courses. But I thought, it would be necessary for all science students studying ICT, especially those who are HSC students. And I hope students will definitely benefit from these slides and be able to learn something about the number system and digital logic gates.

1. Number System
&
Logic Gate
Course Title : Digital Logic Design
Course No : CSE-305
Presented By : Ashfakur Rahman
Reg No : 2018331524
Dept. Of CSE, Sylhet Engineering College, Sylhet

2. Number System
What is Number System?
• The method of writing or expressing a number and
using it to perform mathematical calculations is
called number system.
➢ There are various types of number system in
mathematics or Computer System:

3. Types of Number System

4. B.‘Non Positional’ Number System
What is Non Positional Number System?
• A number system in which the value of a number
does not depend on the position of the digits used
in the number is called a non-positional number
system.
➢ Hieroglyphics used in ancient times, Mayan and
Roman, Tally number system are examples of non-
positional number system.

5. B.‘Non Positional’ Number System
(Hieroglyphics)
(Tally)
(Roman)

6. A.‘Positional’ Number System
What is Positional Number System?
• A number system in which the value of a number
depends on the position of the digits used in the
number is called positional number system.
➢ The positional number system is divided into four
parts based on the base.(Which we have already
seen in slide No.3)

7. ‘Base’ of a Number System
What is the ‘Base’ of a Number System?
• The total number or sum of the basic symbols
used in a number system is called the base of
that number system.
➢ A base is expressed as a subscript (a little below the
right of the number) to indicate which number is
written in which number system.(Number)base

8. A.PositionalNumberSystemataglance

9. 1.Binary Number System
What is Binary Number System?
• The number system in which the two symbols 0
and 1 are used is called the binary number
system. The two basic symbols of the binary
number system 0 and 1 are called bits and a byte
is made up of eight bits.(1011)2
Base: Since 0 and 1 are the two symbols used in the
binary number system, so its base is 2.

10. 1.Binary Number System
Uses: The binary number system is used in
computers or all electronic devices. All electronics
devices can sense only two conditions, the
presence and absence of electricity. The presence
of electricity is called ON, HIGH, TRUE or YES which
indicates logic level 1 and the absence of electricity
is called OFF, LOW, FALSE or NO which indicates
logic level 0. The two basic symbols of the binary
number system 0 and 1 are called bits and a byte is
made up of eight bits.

11. 2.Octal Number System
What is Octal Number System?
• The word ‘octa’ means 8. The number system in which
8 (0,1,2,3,4,5,6,7) symbols are used is called octal
number system. In digital systems, octal number
system is used for accurate and easy representation of
binary numbers in various fields.(167)8
Base: Since 0,1,2,3,4,5,6,7 are the 8 symbols used in the
Octal number system, so its base is 8.

12. 3.Decimal Number System
What is Decimal Number System?
• The word ‘deci’ means 10. The number system in
which 10 (0,1,2,3,4,5,6,7,8,9) symbols are used is
called decimal number system. We usually use
the decimal number system to calculate in our
daily lives.(189)10
Base: Since 0,1,2,3,4,5,6,7,8,9 are the 10 symbols used
in the Decimal number system, so its base is 10.

13. 4.Hexadecimal Number System
What is Hexadecimal Number System?
• The word ‘Hexa’ means 6 and ‘Decimal’ means 10.
The number system in which (6+10)=16
(0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F) symbols are used is
called Hexadecimal number system.(1209A)16
Base: Since 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F are the 16
symbols used in the Hexadecimal number system, so its
base is 16.

14. 4.Hexadecimal Number System
Uses: In digital systems, Hexadecimal
number system is used for accurate and
easy representation of binary numbers in
various fields. Besides, The hexadecimal
number system is used as a code for
different memory addresses and colors.

15. Logic Gate?
A logic gate is a basic building
block of a digital circuit, which
is used to implement a Boolean
function. It is an electronic
circuit which makes logical
decisions based on the
combination of digital signals
present on its inputs. It is an
electronic circuit having one or
more than one inputs and only
one output.

16. Types of Logic Gate

17. Basic Gate
Basic gates which implement the basic
operation of Boolean Algebra. All
compound gates and any logic circuit can
be implemented using basic gates. There
are three types of basic gates in digital
electronics. They are-
1. OR Gate
2. AND Gate
3. NOT Gate

18. OR Gate
OR Gate is a gate of logical addition. That
is, the gate used to perform logical
additions in Boolean algebra is called OR
gate. The OR gate has two or more input
lines and only one output line. If all the
inputs are 0 then only the output will be
0 otherwise the output will be 1.

19. OR Gate(2-input)

20. OR Gate(3-input)

21. AND Gate
AND Gate is a gate of logical multiplication.
That is, the gate used to perform logical
multiplication in Boolean algebra is called
AND gate. The AND gate has two or more
input lines and only one output line. If all
the inputs are 1 then only the output will be
1 otherwise the output will be 0.

22. AND Gate(2-input)

23. AND Gate(3-input)

24. NOT Gate
NOT Gate is a gate of logical inversion/
complementation. That is, the gate used to
perform logical inversion /complementation
in Boolean algebra is called NOT gate. The
NOT gate has only one input line and one
output line. If the input is 1 then the output
will be 0 and if the input is 0 then the
output will be 1.

25. NOT Gate

26. Compound Gate
A gate that is created using two or more basic
gates is called a compound gate. For example-
• AND Gate +NOT Gate = NAND Gate
• OR Gate + NOT Gate = NOR Gate
Compound gates are two types. They are-
1. Universal Gate (NOR & NAND)
2. Exclusive Gate (X-OR & X-NOR)

27. Universal Gate
The gate which can implement all
the basic gates (AND, OR, NOT) as
well as any gate and any circuit is
called a universal gate. NAND and
NOR gates are called universal
gates. This is because only NAND
gate or only NOR gate can
implement all the basic gates
(AND, OR, NOT) as well as any
gate and any circuit. Fig: Universal gate(NAND & NOR)

28. NOR Gate
The Logic NOR Gate is a compound gate which is
combination of the logic OR gate and an NOT gate
connected together in series. By reversing the
output of the OR gate, the output of the NOR gate
is obtained.
Fig: OR Gate + NOT Gate = NOR Gate

29. NOR Gate(2-input)

30. NOR Gate(3-input)

31. NAND Gate
The Logic NAND Gate is a compound gate which is
combination of the logic AND gate and an NOT gate
connected together in series. By reversing the
output of the AND gate, the output of the NAND
gate is obtained.
Fig: AND Gate + NOT Gate = NAND Gate

32. NAND Gate(2-input)

33. NAND Gate(3-input)

34. Exclusive Gates
Two “hybrid” logic gates are called the
Exclusive-OR (X-OR) Gate and its complement
the Exclusive-NOR (X-NOR) Gate.

35. X-OR Gate
The Exclusive OR Gate is abbreviated as the X-
OR Gate. This is a compound gate made up of
AND, OR and NOT gates. The X-OR gate has two
or more input lines and only one output line.
The output is “1” when there are an odd
number of 1’s in the inputs, otherwise it is 0.
The X-OR operation is represented by ⊕
symbol. If A and B are the inputs of X-OR gate,
then output F will be-
F = A⊕B = A´B + AB´

36. X-OR Gate
F = A⊕B = A´B + AB´
Fig: Implementation of XOR gate using Basic gates

37. X-OR Gate(2-input)

38. X-OR Gate(3-input)

39. X-NOR Gate
The Exclusive NOR Gate is abbreviated as the
X-NOR Gate. It is combination of the X-OR gate
and the NOT gate connected together in series
that is also the reverse or complementary of
the Exclusive-OR gate. This is a compound
gate made up of AND, OR and NOT gates. The
X-NOR gate has two or more input lines and
only one output line. An even number of logic
“1’s” on its inputs gives a logic “1” at the
output, otherwise it is 0. The output-
F = (A⊕B)´ = A´B´ + AB

40. X-NOR Gate
Fig: Implementation of X-NOR gate using Basic gates
F = (A⊕B)´ = A´B´ + AB

41. X-NOR Gate(2-input)

42. X-NOR(3-input)