Conversion binary to decimal, Decimal to binary , octal to binary, hexadecimal to binary, binary to hex , decimal to hex ................ All conversion .

1. Number system

2. Decimal
 The Decimal numeral system has ten as
its base .
 It is numerical base most widely used by
modern civilizations.
 Base 10
 Consists of digits 0 to 9
 Example:
decimal:1 5 0 100 -250 5567
Shovo

3. Binary
 Binary uses only 2 digits which are 0
and 1 and is also called base 2.
 Consists of digits 0 and 1
 Example: (1001)2
Shovo

4. Octal
 Octal uses 8 digits which are
0,1,2,3,4,5,6,7 .
 It is also called base 8.
 The First digit must be 0.
 Example: 2758
Shovo

5. Hexadecimal
 The word hexadecimal is made up of
2 parts which are hex(6) and
decimal(10).
 Hexadecimal is sometimes called hex
or base 16.
 To get 16 digits we have to use
letters of the alphabet and those 16
are 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F.
 Example: 7F16
Shovo

6. Data Conversation

7. Binary
 Now,
How to convert decimal to binary ?
How to return binary to decimal?
Suppose a decimal number is 81.

8. Decimal to Binary
 1st the decimal divided by 2
Akmol

9. Decimal to Binary
2nd count the modulas from
down to up.
Means
Akmol

10. Decimal to Binary
7th
6th
5th
4th
3rd
2nd
1st
 So the binary is
 (1010001)2
Akmol

11. Binary to Decimal
 Now binary to decimal
 From right to left every digit will be
counted.
 Every digit should be multiply with
2.because binary base is 2.
 And It’s power will be started from
zero & in per digit it(power) will
increase 1 rapidly right to left
rapidly.
Akmol

12. Binary to Decimal
 The answer of multiply of every digit
will be added to each other.
 These we can get our desired
decimal number.
Akmol

13. example
Akmol

14. Conversation of Octal
How to convert decimal to octal?
How to return octal to decimal ?
Tarek

15. Conversation of Octal
 There is no method to covert decimal
to direct octal.
 1st the number should convert in
binary and then we can convert it in
octal.
 But when we can direct covert the
octal number to decimal.
Tarek

16. Binary to octal
 To be converted in octal , from right
to left we should count 3 digits of
that binary number as a set.
 Suppose the binary number is
• (1010001)2
 Example Figure is
 1 010 001
Tarek

17. Binary to octal
 1 010 001
 Here two digits less.
 In this cage we count “0” before that
number to fill the set.
 Means 001
 here we take two zero to fill the set .
Tarek

18. Binary to octal
 Here in example , we have 3 sets. Now
every digit of a set should multiple with
two. Because binary base is two.
 Now power of “two” should set serially
which starts from zero.. And then 1 , then
two…
 At last we should calculate the result of
the sets and calculate addition of the
sets .
 the answers should place side by side
from right to left to create a number.
Tarek

19. Example
 001 010 001
 001
 0*2^2 +0*2^1+1*2^0
 =0+0+1
 =1
 010
 0*2^3 +1*2^1+0*2^0
 =0+2+0
 =2
 001
 001
 0*2^2 +0*2^1+1*2^0
 =0+0+1
 =1
 if we set all this numbers side by side , we got 121
Tarek

20. Octal to Binary
 To convert octal to binary,wecount every
digit of octal from right to left anddivided
by binary base.
 Binary base is 2 and octal base is
8.so2^3=8
 So ,every digit of octal number maximum
value of 3 digit in binary format. if it less
then 3 digit fill with 0 before that digits.
 Then arrange binaryvalue of every digit
from right to left. If that digit have use
less 0 beforewe cut them and get desire
number.

21. Octal to Binary
 here , (121)
 8
 Now 2 1 2 2 2 1
 0-1 1-0 0-1
 0-1
 Found 1 01 2 010 1 01
 here two digit less
 So , 1 001 2 010 1 001
 Now arrange the binary right to left & found.
 (121) 0010100001
 8
 (121) 10100001
 8

22. Octal to decimal
 Count every digit and multiply with octal
base ( 8) with each.
 now we should insert the base power
from right to left
 Then calculate the answer and also
calculate the additional answer,
 This answer is our desired decimal
number.

tarek

23. Octal to decimal
 Example
Tarek

24. Conversation of Hexadecimal
 How to convert decimal to hexadecimal ?&
 How to return hexadecimal to decimal ?
Pradipta

25. Conversation of Hexadecimal
 The formula of Number conversation of octal &
hexadecimal is very close.
 For convert directly decimal to hexadecimal,
there is no method.
 1st we should convert the decimal number to
binary, then binary to hexadecimal.
 But same as octal it also directly convert
hexadecimal to decimal.
Pradipta

26. Decimal to Hexadecimal
 Suppose the decimal number is= 81 &
 it’s binary is (1010001)2
 To be converted into hexadecimal, from right to
left we should count 4 digits of that binary
number as a set.
 Example Figure is
 101 0001
Pradipta

27. Binary to Hexadecimal
 101 0001

 Here one digits less.
 In this cage we count “0” before that
number to fill the set.
 Means 0101
 here we take one zero to fill the set .
Pradipta

28. Binary to Hexadecimal
 Here in example , we have 2 sets. Now every
digit of a set should multiple with two. Because
binary base is two.
 Now power of “two” should increase rapidly count
from zero. At last we should calculate the result
of the sets and calculate addition of the sets .
 the answers should place side by side from right
to left to create a number.
Pradipta

29. Binary to Hexadecimal
 Now (1010001)2
 0001
 3 2 1 0
 =0x2+0x2+0x2+1x2
 =0+0+0+1
 =1
 0101
 3 2 1 0
 =0x2+1x2+0x2+1x2
 =0+4+0+1
 =5
 arrange the number right to left…..get 51
 Now ,we get the hexadecimal- (51)16
pradipta

30. Hexadecimal to binary
 To convert hexadecimal to binary, we
count every digit of hexadecimal from right
to left and divided by binary base.
 Binary base is 2 and hexadecimal base is
16.so 2^4=16
 So ,every digit of hexadecimal number
maximum value of 4 digit in binary format.
if it less then 4 digit fill with 0 before that
digits.
 Then arrange binary value of every digit
from right to left. If that digits have
useless 0 before we cut them and get
desire number.

31. Hexadecimal to binary
 here , (51)
 16
 Now 2 5 2 1
 2 2-1 0-1
 1-0
 Found 5 101 1 01
 here some digit less
 So , 5 0101 1 0001
 Now arrange the binary right to left & found.
 (51) 010100001
 16
 (121) 10100001
 16

32.  Hexadecimal to
octal
 It is not possible,
1st hexadecimal
number convert
into binary then
octal.
Octal to Hexadecimal
 It is not possible,
1st octal number
convert into binary
then hexadecimal.

33. Hexadecimal to Decimal
 Now ,
 Count every digit and multiply with
hexadecimal base (16) with each &
increase power from right to left
 Then calculate the multiply and also add
the answer.
 This answer is our desired decimal
number.
Pradipta

34. Hexadecimal to Decimal
 now,
 (51)16
1 0
 =5x16 + 1x16
 =80+1
 =81
Pradipta

35. Thanks all .
Made by-
Pradipta, Tarek, Yusuf &
shovo.