Hexadecimal Number System (Base 16 Number System)
In the hexadecimal system, numbers are written or represented with base 16. In the
hexadecimal system, the numbers are first represented just like in the decimal
system, i.e. from 0 to 9. Then, the numbers are represented using the alphabet from
A to F. The below-given table shows the representation of numbers in the
hexadecimal number system.
Example 1:
Convert (1056)16 to an octal number.
Solution:
Given, 105616 is a hex number.
First we need to convert the given hexadecimal number into decimal number
(1056)16
= 1 × 163 + 0 × 162 + 5 × 161 + 6 × 160
= 4096 + 0 + 80 + 6
= (4182)10
Now we will convert this decimal number to the required octal number by
repetitively dividing by 8.
Therefore, taking the value of the remainder from bottom to top, we get;
(4182)10 = (10126)8
Therefore,
(1056)16 = (10126)8
Example 2:
Convert (1001001100)2 to a decimal number.
Solution:
(1001001100)2
= 1 × 29 + 0 × 28 + 0 × 27 + 1 × 26 + 0 × 25 + 0 × 24 + 1 × 23 + 1 × 22 + 0 × 21 +
0 × 20
= 512 + 64 + 8 + 4
= (588)10
Example 3:
Convert 101012 into an octal number.
Solution:
Given,
101012 is the binary number
We can write the given binary number as,
010 101
Now as we know, in the octal number system,
010 → 2
101 → 5
Therefore, the required octal number is (25)8
Example 4:
Convert hexadecimal 2C to decimal number.
Solution:
We need to convert 2C16 into binary numbers first.
2C → 00101100
Now convert 001011002 into a decimal number.
101100 = 1 × 25 + 0 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 0 × 20
= 32 + 8 + 4
= 44
