ConvertOnlineOctal to Hex Converter
Converting an Octal Number to Hexadecimal
The octal numeral system (base-8) uses digits from 0 to 7, while the hexadecimal system (base-16) uses sixteen distinct symbols: 0-9 to represent values zero to nine, and A-F to represent values ten to fifteen. Converting an octal number to its hexadecimal equivalent involves two main steps: first, converting the octal number to a binary number, and then converting the binary number to hexadecimal.
Each octal digit corresponds to exactly three binary digits (bits), and each hexadecimal digit corresponds to four binary digits. This means that a direct conversion from octal to hexadecimal involves first converting the octal number to binary, grouping the binary digits into sets of four, and then converting each group to its corresponding hexadecimal digit.
For example, the octal number 345 can be converted to hexadecimal by first converting it to binary:
3 = 011, 4 = 100, 5 = 101
The binary equivalent is 011100101. Next, group the binary digits into sets of four, starting from the right:
0011 1001 01
Adding a leading zero to the last group, we get:
0011 1001 0101
Finally, convert each group to its corresponding hexadecimal digit:
0011 = 3, 1001 = 9, 0101 = 5
Thus, the hexadecimal equivalent of 345 is 195.
Examples
Let’s explore some examples to understand how to convert octal numbers to their hexadecimal equivalents.
1. Convert the octal number 345 to hexadecimal.
Answer
First, we identify the given number:
Given:
- Octal: 345
Next, we convert each octal digit to its binary equivalent:
Steps:
- 3 = 011
- 4 = 100
- 5 = 101
The binary equivalent is 011100101. We then group the binary digits into sets of four, starting from the right:
Steps:
- 0011 1001 0101
Finally, convert each group to its corresponding hexadecimal digit:
- 0011 = 3
- 1001 = 9
- 0101 = 5
The final hexadecimal value is:
Hexadecimal Equivalent:
195
Result:
∴ The hexadecimal equivalent of the octal number 345 is 195.
2. Convert the octal number 52 to hexadecimal.
Answer
We start by identifying the number:
Given:
- Octal: 52
Next, we convert each octal digit to its binary equivalent:
Steps:
- 5 = 101
- 2 = 010
The binary equivalent is 101010. We then group the binary digits into sets of four, starting from the right, and add leading zeros as needed:
Steps:
- 0001 01010
Finally, convert each group to its corresponding hexadecimal digit:
- 0001 = 1
- 01010 = A (after adjusting for four bits)
The final hexadecimal value is:
Hexadecimal Equivalent:
1A
Result:
∴ The hexadecimal equivalent of the octal number 52 is 1A.
3. Determine the hexadecimal equivalent of the octal number 701.
Answer
First, we identify the given number:
Given:
- Octal: 701
Next, we convert each octal digit to its binary equivalent:
Steps:
- 7 = 111
- 0 = 000
- 1 = 001
The binary equivalent is 111000001. We then group the binary digits into sets of four, starting from the right, and add leading zeros as needed:
Steps:
- 0111 0000 01
Finally, convert each group to its corresponding hexadecimal digit:
- 0111 = 7
- 0000 = 0
- 0001 = 1
The final hexadecimal value is:
Hexadecimal Equivalent:
701
Result:
∴ The hexadecimal equivalent of the octal number 701 is 701.
4. Convert the octal number 16 to hexadecimal.
Answer
We start by identifying the number:
Given:
- Octal: 16
Next, we convert each octal digit to its binary equivalent:
Steps:
- 1 = 001
- 6 = 110
The binary equivalent is 001110. We then group the binary digits into sets of four, starting from the right, and add leading zeros as needed:
Steps:
- 0001 110
Finally, convert each group to its corresponding hexadecimal digit:
- 0001 = 1
- 110 = 6
The final hexadecimal value is:
Hexadecimal Equivalent:
16
Result:
∴ The hexadecimal equivalent of the octal number 16 is 16.