To convert an octal number (base 8) to a hexadecimal number (base 16), the easiest method is to first convert the octal number to binary and then convert the binary number to hexadecimal.
Steps for Conversion:
Convert the octal number to binary.
Each octal digit is equivalent to a 3-bit binary number.
Group the binary digits into sets of 4 bits (starting from the right). If the leftmost group has fewer than 4 bits, pad it with leading zeros.
Convert each 4-bit group to its hexadecimal equivalent.
Example:
Let's convert the octal number 345 to hexadecimal.
Step 1: Convert octal to binary
3 in octal = 011 in binary
4 in octal = 100 in binary
5 in octal = 101 in binary
So, the binary equivalent of 345 in octal is 011 100 101.
Step 2: Group binary digits into sets of 4 bits
We group the binary digits as follows:
0111 (add one leading 0 to make 4 bits)
0010
0101
So, we get the binary number 0111 0010 0101.
Step 3: Convert binary to hexadecimal
0111 in binary = 7 in hexadecimal
0010 in binary = 2 in hexadecimal
0101 in binary = 5 in hexadecimal
Thus, the hexadecimal equivalent of the octal number 345 is 725.
Final Answer:
The octal number 345 is equal to the hexadecimal number 725.