ConvertOnlineBinary to Octal Converter
Converting a Binary Number to Octal
Binary and octal numeral systems are commonly used in computing. The binary system (base-2) uses only two digits: 0 and 1, while the octal system (base-8) uses eight distinct digits: 0 to 7. Octal numbers provide a more compact way to represent binary values, which is particularly useful in digital electronics and programming.
To convert a binary number to its octal equivalent, the binary number is first grouped into sets of three bits, starting from the right. Each group of three bits is then converted to its corresponding octal digit. If the number of bits is not a multiple of three, you can add leading zeros to the leftmost group to make it three bits long.
For example, the binary number 1101101 can be converted to octal by following these steps:
001 101 101
The first group, 001, is equivalent to 1 in octal, the second group, 101, is equivalent to 5 in octal, and the third group, 101, is also equivalent to 5 in octal. Therefore, the octal equivalent of 1101101 is 155.
Examples
Let’s explore some examples to understand how to convert binary numbers to their octal equivalents.
1. Convert the binary number 1101101 to octal.
Answer
First, we identify the given number:
Given:
- Binary: 1101101
Next, we group the binary digits into sets of three, starting from the right. Since the number of digits is not a multiple of three, we add leading zeros to the left:
Steps:
- 001 101 101
We then convert each group to its corresponding octal digit:
- 001 = 1
- 101 = 5
- 101 = 5
The final octal value is formed by concatenating these digits:
Octal Equivalent:
155
Result:
∴ The octal equivalent of the binary number 1101101 is 155.
2. Convert the binary number 10110 to octal.
Answer
We start by identifying the number:
Given:
- Binary: 10110
Next, we group the binary digits into sets of three, starting from the right. Since the number of digits is not a multiple of three, we add a leading zero to the left:
Steps:
- 010 110
We then convert each group to its corresponding octal digit:
- 010 = 2
- 110 = 6
The final octal value is formed by concatenating these digits:
Octal Equivalent:
26
Result:
∴ The octal equivalent of the binary number 10110 is 26.
3. Determine the octal equivalent of the binary number 111111.
Answer
First, we identify the given number:
Given:
- Binary: 111111
Next, we group the binary digits into sets of three, starting from the right:
Steps:
- 111 111
We then convert each group to its corresponding octal digit:
- 111 = 7
- 111 = 7
The final octal value is formed by concatenating these digits:
Octal Equivalent:
77
Result:
∴ The octal equivalent of the binary number 111111 is 77.
4. Convert the binary number 100011 to octal.
Answer
We start by identifying the number:
Given:
- Binary: 100011
Next, we group the binary digits into sets of three, starting from the right:
Steps:
- 100 011
We then convert each group to its corresponding octal digit:
- 100 = 4
- 011 = 3
The final octal value is formed by concatenating these digits:
Octal Equivalent:
43
Result:
∴ The octal equivalent of the binary number 100011 is 43.