This video is about number system and there is some important definitions... hope so it will be help full for you!

2. By:
Iqra Sundip Yasin
1450-213001
NUMBER SYSTEM
&
DEFINATIONS

3. Digital Number System
 Many number system are in use in digital technology. The
most common are the decimal, binary, octal, hexadecimal
system.

4. OTHER NUMBER SYSTEM
 Base-2 binary system
 Base3 tritary system Base-11 undecimal system
 Base-4 quaternary system Base-12 duodecimal system
 Base-5 quinary system Base-13 tridecimal system
 Base-6 senary system Base-14 tetradecimal system
 Base-7 septenary system Base-15 pentadecimal system
 Base-8 octal system Base-16 hexadecimal system
 Base-9 nonary system
 Base-10 decimal system Base-20 The vigesimal system
Base-36 hexatridecimal system

5. The decimal system is composed of
10 symbols. These 10 symbols are
0,1,2,3,4,5,6,7,8,9; using these
symbols as digits of a number of a
number. The decimal system also
called base 10 system because it has
10 digits, has evolved naturally as a
result of the fact that people have 10
finger .
In fact, the word “digit” is derived
from the Latin word for “finger.”

6. Positional Notation
 The decimal system is a positional –value system in which the
value of a digit depends on its position….
 642 in base 10 positional notation is:
6 x 102 = 6 x 100 = 600
+ 4 x 101 = 4 x 10 = 40
+ 2 x 10º = 2 x 1 = 2 = 642 in base 10
The power
indicates
the position of
the number

7. MSD & LSD
Stands for Most significant digit and least significant digit
respectively e.g. 2735.214.
2 carries the most weight or value so 2 is MSD and 4 carries the
least weight or value so 4 is LSD .

8. CONVERSION
Decimal to binary , octal and hexadecimal
 Conversion from decimal system into other system. It involves using
successive division by the radix until the dividend reaches 0. At each division, the remainder
provides a digit of the converted number, starting with the least significant digit.
 For example: convert 3710 to binary
37 / 2 = 18 remainder 1 (least significant Bit)
18 / 2 = 9 remainder 0
9 / 2 = 4 remainder 1
4 / 2 = 2 remainder 0
2 / 2 = 1 remainder 0
1 / 2 = 0 remainder 1 (most significant Bit)
The resulting binary number is: 100101 THAT WE START FROM MSB TO LSB

9. EXAMPLE: CONVERT (177)10 TO OCTAL
Conversion of decimal fraction to octal fraction is carried out in the same
manner as decimal to binary except that now the multiplication is carried
out by 8.
SOLUTION:
177 / 8 = 22 remainder is 1
22 / 8 = 2 remainder is 6
2 / 8 = 0 remainder is 2
The resulting binary number is: (261)8

10. Example: convert (4768)10 to hex.
Solution:
= 4768 / 16 = 298 remainder 0
= 298 / 16 = 18 remainder 10 (A)
= 18 / 16 = 1 remainder 2
= 1 / 16 = 0 remainder 1
The resulting binary number is: (12A0)16

11. What if 642 has the base of 13?
6 x 132 = 6 x 169 = 1014
+ 4 x 131 = 4 x 13 = 52
+ 2 x 13º = 2 x 1 = 2
2+52+1014 = 1068 in base 10
642 in base 13 is equivalent to 1068
in base 10

12. Binary Number System
 Base = 2
 2 digits { 0, 1 }, called binary digits or “bits”
 Weights
 Weight = (Base) Position
 Formal Notation
Groups of bits 4 bits = Nibble
8 bits = Byte

13. Converting Binary to Decimal
 What is the decimal equivalent of the binary number 1101110?
1 x 26 = 1 x 64 = 64
+ 1 x 25 = 1 x 32 = 32
+ 0 x 24 = 0 x 16 = 0
+ 1 x 23 = 1 x 8 = 8
+ 1 x 22 = 1 x 4 = 4
+ 1 x 21 = 1 x 2 = 2
+ 0 x 2º = 0 x 1 = 0
= 110 in base 10

14. Conversion of binary to octal and hex Conversion
 Conversion of binary numbers to octal and hex simply requires
grouping bits in the binary numbers into groups of three bits for
conversion to octal and into groups of four bits for conversion to
hex.
 Groups are formed beginning with the LSB and progressing to the
MSB.
 10101011 10 101 011
2 5 3
 10101011 1010 1011
A(10) B(11)

15. Conversion of binary to octal

16. Conversion of binary to hexadecimal
 Convert the binary number 0110101110001100 to hexadecimal
 Divide into groups of 4 digits 0110 1011 1000 1100
Convert each group to hex digit 6 B(11) 8 C(12)
6B8C in hex

17. Calculator Hint
 If you use a calculator to perform the divisions by 2, you
can tell whether the remainder is 0 or 1 by whether or not
the result has a fractional part. For instance, 25/2 would
produce 12.5. Since there is a fractional part (.5 ), the
remainder is a 1. If there were no fractional part, such as
12/2=6 then the remainder would be 0.

18. Octal refers to a numbering system that has a base
of eight. This means it only uses the eight numerals
0,1,2,3,4,5,6,7 for each digit of a number.

19. Conversion:
Converting Octal to Decimal:
What is the decimal equivalent of the octal number 642?
6 x 82 = 6 x 64 = 384
+ 4 x 81 = 4 x 8 = 32
+ 2 x 8º = 2 x 1 = 2
= 418 in base 10
 Example: convert (632)8 to decimal
= (6 x 82) + (3 x 81) + (2 x 80)
= (6 x 64) + (3 x 8) + (2 x 1)
= 384 + 24 + 2
= (410)10

20. 1) Convert (634)8 to binary equivalent?
Sol.
6 3 4
110 011 100 .
Binary number = (110011100)2
2) Convert (615)8 to hexadecimal equivalent?
Sol.
Step1 octal to binary
6 1 5
110 001 101
Binary number = 110001101
Step2 binary to hexadecimal
0001 1000 1101
1 8 D
.: Hexadecimal number = (18D)16

21. Calculator Hint
 If a calculator is used to perform the division , the result will
include a decimal fraction instead of a remainder. The
remainder can be obtained, However, by multiplying the
decimal fraction by 8, for example 266/8 produces 33.25.The
remainder becomes 0.25 * 8 =2.
 We need this hint when we convert decimal system into octal
system..

22. Hexadecimal number system

23. Convert (BEEF)16 into ( )10

24. CONVERT (9F2)16 INTO ( )2 ?
Shorthand method to representing binary numbers…(8421)
(9F2)16 = 9 F 2
1001 1111 0010
SO binary number is= 100111110010
Convert (25B)16 to octal equivalent?
Sol.
Step1 hexadecimal to binary
2 5 B
0010 0101 1011
Binary number = 001001011011
Step2 binary to octal
001 001 011 011
1 1 3 3
Octal number = (1133)8

25. link:
http://www.translatorscafe.com/cafe/EN/units-converter/numbers/2-1/octal-binary/

26. DEFINATIONS:
 Digital Signal: A digital
signal is a physical
signal that is a representation
of a sequence of discrete values.
 Analog Signal: Analog signal
is a continuous signal w.r.t
time. An Analog signal have
its changing value at every
instant of time

27. Active high and low:
Active high: It can call as positive
logic. The high voltage +5v
represent logic high that is 1 and
lower 0v represent the logic low
that is 0.
Active low: it can call as negative
logic . The higher voltage
represent as logic low that is o
and lower voltage represent as
logic high that is 1..

29. Duty Cycle
A duty cycle is the percentage of
one period in which a signal is active. A
period is the time it takes for a signal to
complete an on-and-off cycle. As a
formula, a duty cycle may be expressed as:
D=T/P *100
where is the duty cycle, is the time the
signal is active, and is the total period of
the signal. Thus, a 50 % duty cycle means
the signal is on 50 % of the time but off
50% of the time.

30. Flip Flop
Memory device capable of storing a
logic level.
Types of FF:
i. S-R FF
ii. J-K FF
iii. D FF
iv. T FF

31. Fan in and out
 Fan-in is a term that defines the maximum number of digital
inputs that a single logic gate can accept. A typical logic gate
has a fan-in of 1 or 2.
 Fan-out is a term that defines the maximum number of digital
inputs that the output of a single logic gate can feed.
OR
 The maximum number of logic inputs that an output can drive
reliably called fan out.

34. THANK YOU