Number System
Let's Start
NUMBER SYSTEM
If we think about number then first thing come in our mind is "1,2,3,4....9". According to Wikipedia
" A number system is a collection of various symbols which are called digits ''
So Now the question is why we going to study that or number system in this time ?
If we go in past and compare future every thing is based on ' Numbers '
Example : Now day's every thing is or almost every thing is connected with computer or machine and we all know . That any machine or computer based or understand binary numbers 0,1 that is why it is and it was important in past.
Counting system
In past the problem was that. There sheep and cow get always mixed up with each others so they end up fighting always .... so they fond a solution that was the starting of counting.When ever any sheep or cow go out side they store some rock in the box
Example : if 10 sheep go out from house then they keep 10 stone and when they come they mines the rock that's how the start and after that there come another counting method
Decimal : The number that having base 10 and symbols 0 to 9 these are commonly used in our daily life.
Tally marks & Hash marks
| Telly marks |
and after that then the symbols formed
Then start the counting or numbers till now shown in pitcher
like we see in the pitcher 0 to 9 number go the it change and come next number the start 10 to 19 then 20 to 29 continue ... so this is counting.
Types of number system
 |
| Types of number system |
Example (165)10
Octal : The number that having base 8 and symbols 0,7
Example (245)8
Hexadecimal : The number that having base 16 and symbols 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
Example (A5)16
Binary : The number that having base 2 and symbols 0,1
Example (10100101)2
Now we know all about the types of number system next we study there conversions
In this part we do some conversions
- Binary to Decimal & Decimal to Binary
- Octal to Decimal & Decimal to Octal
- Octal to Binary & Binary to Octal
- Hexadecimal to Decimal, Binary & Octal / Decimal, Binary & Octal to Hexadecimal
altos of people get confuse in these conversions .
1st Binary to Decimal & Decimal to Binary
- Binary to Decimal
In this remember we have to multiply with 2 and add them we get decimal number
Example
(111000)2 ➝ (?)10
5 4 3 2 1 0
1 1 1 0 0 0
↓ ↓ ↓ ↓ ↓ ↓
(2)5 X 1+ (2)4 X 1 + (2)3 X 1 + (2)2 X 0+ (2)1 X 0 + (2)0 X 0
32+16+8+0+0+0
(56)10
- Decimal to Binary
In this we have to divide base 10 by 2 and we get binary form
Example
(56)10 → (?)2
(111000)2
2Nd Octal to Decimal & Decimal to Octal
- Decimal to Octal
In this we just divide base 10 by 8 and we get Octal form
Example
In this just have to multiply by 8 and add we get the 10 base form
Example
(165)10 → (?)8
(245)8
- Octal to Decimal
Example
(245)8 ➝ (?)10
2 1 0
2 4 5
↓ ↓ ↓
(8)2 X 2 + (8)1 X 4 + (8)0 X 5
64 X 2 + 8 X 4 + 1 X 5
128 + 32 + 5
(165)10
- Octal to Binary and Binary to Octal
- Octal to Binary
Example
(245)8 ➝ (?)2
2 4 5
2 4 5
↓ ↓ ↓
10 100 101
(10100101)2
- Binary to Octal
In this you have to be careful because you have to make 3 pairs of binary number in Octal conversion " like you see in 010, 100, 101 they are in pairs of 3 " If they are not in pair then we add 0 zero in Left side .
(10100101)2 ➝ (?)8010 100 101
↓ ↓ ↓
2 4 5
(245)8
- Hexadecimal to Decimal, Binary & Octal / Decimal, Binary & Octal to Hexadecimal
In Hexadecimal all conversions are same but values will change 9, you have to right A,B,C,D,E,F. Because hexadecimal base is 16 and symbols are 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
"10 = A , 11 = B , 12 = C , 13 = D , 14 = E , 15 = F "
In octal you have to first convert the in binary and the change in hexadecimal
remember when ever you change binary in to hexadecimal yo have make 4 pairs of binary numbers
Example
(10100101)2 ➝ (?)16
1010 0101
1010 0101
↓ ↓
A 5
(A5)16
Thank you
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