Hello friends,Previously we have discussed about probability examples and today i am going to teach you Number system in mathematics which constitutes a large space in cbse text books. As we talk about computers it works on only two digits 0 and 1, called binary numbers. Computer can only capable of manipulating binary numbers. If we want to understand how computer works, we should be able to use binary number system. But in order to work well as a computer professional we should know all types of number systems and way to convert between each other, If anyone wants they can take help of online tutoring. Because many times we need to convert one number system into other.
Types of Numbers
1. Decimal System
2. Binary System
3. Octal System
4. Hexadecimal System
Decimal System
Base 10
Digits - 0 to 9
Also called the positional number system. In decimal number system each digit is multiplied by the power of 10 depending on the position of the digit, which increases as we move from right to left, where first right most digit has power 0.
Example: 78610
786 = 7 * 102 + 8*101 + 6*100
= 700 + 70 + 6
Binary System
Base 2
Digit – 0 and 1
In Binary number system there can be only two possible values 0 and 1, often called as “bit”. Number of bits used in binary number represents the number. Power of 2 is used rather than 10 as in decimal number.
Example: 100102 number of bits =5, 1110112 number of bits =6
Octal System
Base 8
Digits – o to 7
Power of 8 is used to represent or convert from any number system into octal.
Example : 2238, 4568,5578
Hexadecimal Number
Base 16
Digits – 0 to 9 and a to f
Power of 16 is used to represent number in this number system. Hexadecimal is the grouping of binary number that is hexamdecimal no can be broken into two parts of 4bits.
Example: 2AF416, 456AF16 (know more about numbers, here),
Conversion
We will see how to convert one number system into other number system.
Example: 11101 = ?10
Binary to Decimal
1*25 + 1*24 + 1*23 + 1*22 + 0*21 + 1*20
32 + 16 + 8 + 4 + 0 + 1
61
9310 = ?2
Decimal to Binary
93/2 = 46 remainder 1 (Least significant bit)
46/2 = 23 remainder 0
23/2 = 11 remainder 1
11/2 = 5 remainder 1
5/2 = 2 remainder 1
2/2 = 1 remainder 0
1/2 = 0 remainder 1 ( most significant bit)
We write it from msb to lsb
Result = 1011101
Octal to decimal
7548 into ?10
=7x82 + 7x81 + 7x80
=448 + 56 + 7
=511
Decimal to Octal
26410 = ?8
264/8 = 24 remainder 3
24/8 = 0 remainder 3
Result = 33
Hexa to Decimal
2CD16 = ?10
2x162 + Cx161 + Dx160
64 + 12x16 + 13x1
64 + 192 + 13
26910
Decimal to hexa
19210 = ?16
192/16 = 57 remainder 9
57/16 = 3 remainder 9
3/16 = 0 remainder 3
Result = 399
We can use a table to show the relation between all the number system we have.
This table can be simply use to convert one number system into another .
This is all about number system and conversion and if anyone want to know about Properties of Irrational Numbers then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as Rationalizing the Denominator in the next session here.
Types of Numbers
1. Decimal System
2. Binary System
3. Octal System
4. Hexadecimal System
Decimal System
Base 10
Digits - 0 to 9
Also called the positional number system. In decimal number system each digit is multiplied by the power of 10 depending on the position of the digit, which increases as we move from right to left, where first right most digit has power 0.
Example: 78610
786 = 7 * 102 + 8*101 + 6*100
= 700 + 70 + 6
Binary System
Base 2
Digit – 0 and 1
In Binary number system there can be only two possible values 0 and 1, often called as “bit”. Number of bits used in binary number represents the number. Power of 2 is used rather than 10 as in decimal number.
Example: 100102 number of bits =5, 1110112 number of bits =6
Octal System
Base 8
Digits – o to 7
Power of 8 is used to represent or convert from any number system into octal.
Example : 2238, 4568,5578
Hexadecimal Number
Base 16
Digits – 0 to 9 and a to f
Power of 16 is used to represent number in this number system. Hexadecimal is the grouping of binary number that is hexamdecimal no can be broken into two parts of 4bits.
Example: 2AF416, 456AF16 (know more about numbers, here),
Conversion
We will see how to convert one number system into other number system.
Example: 11101 = ?10
Binary to Decimal
1*25 + 1*24 + 1*23 + 1*22 + 0*21 + 1*20
32 + 16 + 8 + 4 + 0 + 1
61
9310 = ?2
Decimal to Binary
93/2 = 46 remainder 1 (Least significant bit)
46/2 = 23 remainder 0
23/2 = 11 remainder 1
11/2 = 5 remainder 1
5/2 = 2 remainder 1
2/2 = 1 remainder 0
1/2 = 0 remainder 1 ( most significant bit)
We write it from msb to lsb
Result = 1011101
Octal to decimal
7548 into ?10
=7x82 + 7x81 + 7x80
=448 + 56 + 7
=511
Decimal to Octal
26410 = ?8
264/8 = 24 remainder 3
24/8 = 0 remainder 3
Result = 33
Hexa to Decimal
2CD16 = ?10
2x162 + Cx161 + Dx160
64 + 12x16 + 13x1
64 + 192 + 13
26910
Decimal to hexa
19210 = ?16
192/16 = 57 remainder 9
57/16 = 3 remainder 9
3/16 = 0 remainder 3
Result = 399
We can use a table to show the relation between all the number system we have.
| Decimal | Hexadecimal | Octal | binary |
| 0 | 0 | 00000000000 | 0000 |
| 1 | 1 | 00100000001 | 0001 |
| 2 | 2 | 00200000010 | 0010 |
| 3 | 3 | 00300000011 | 0011 |
| 4 | 4 | 00400000100 | 0100 |
| 5 | 5 | 00500000101 | 0101 |
| 6 | 6 | 00600000110 | 0110 |
| 7 | 7 | 00700000111 | 0111 |
| 8 | 8 | 01000001000 | 1000 |
| 9 | 9 | 01100001001 | 1001 |
| 10 | A | 01200001010 | 1010 |
| 11 | B | 01300001011 | 1011 |
| 12 | C | 01400001100 | 1100 |
| 13 | D | 01500001101 | 1101 |
| 14 | E | 01600001110 | 1110 |
| 15 | F | 01700001111 | 1111 |
This is all about number system and conversion and if anyone want to know about Properties of Irrational Numbers then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as Rationalizing the Denominator in the next session here.
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