Convert the octal number given below to hexadecimal number:
(7654) 8
Answer:
Answer by student
The hexadecimal equivalent of the octal number (7654) 8 is (F9C) 16
Detailed answer by teachoo
To convert an octal number to a hexadecimal number, we need to follow these steps:
- Convert the octal number to a binary number by replacing each octal digit with its equivalent 3-bit binary representation.
- Group the binary digits into groups of 4 bits from right to left. If the leftmost group has less than 4 bits, add leading zeros to make it 4 bits.
- Convert each group of 4 bits to its equivalent hexadecimal digit by using the following table:
|
Binary |
Hexadecimal |
|
0000 |
0 |
|
0001 |
1 |
|
0010 |
2 |
|
0011 |
3 |
|
0100 |
4 |
|
0101 |
5 |
|
0110 |
6 |
|
0111 |
7 |
|
1000 |
8 |
|
1001 |
9 |
|
1010 |
A |
|
1011 |
B |
|
1100 |
C |
|
1101 |
D |
|
1110 |
E |
|
1111 |
F |
- Write the hexadecimal digits in the same order as the binary groups. For example, 0001 in binary is 1 in hexadecimal, 0101 in binary is 5 in hexadecimal, and so on.
Here is an example of how to convert (7654) 8 to hexadecimal:
- Convert (7654) 8 to binary by replacing each octal digit with its equivalent binary representation:
(7654) 8 = (11111010100) 2
- Group the binary digits into groups of 4 bits from right to left. Add leading zeros if necessary:
(11111010100) 2 = (0001 1111 0101 00) 2
- Convert each group of 4 bits to its equivalent hexadecimal digit using the table:
(0001) 2 = (1) 16
(1111) 2 = (F) 16
(0101) 2 = (5) 16
(00) 2 = (0) 16
- Write the hexadecimal digits in the same order as the binary groups:
(0001)(1111)(0101)(00) 2 = (1)(F)(5)(0) 16
- Remove any leading zeros from the hexadecimal number:
(10)(F)(5)(0) 16 = (F50) 16
So, the octal number (7654) 8 is equivalent to the hexadecimal number (F50) 16 .
