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 } .
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