How to convert decimal to octal and vice versa?
2 Answers
Converting between decimal (base 10) and octal (base 8) systems involves specific methods for each direction. Here’s a detailed breakdown of both processes:
### Converting Decimal to Octal
1. **Divide by 8**: Start with the decimal number you want to convert. Divide the number by 8.
2. **Record the Remainder**: Keep track of the remainder. This will be one of the digits in the octal number. If your division results in a negative number or zero, stop here.
3. **Repeat the Division**: Take the quotient (the result of the division) and repeat the process: divide the quotient by 8, recording the new remainder.
4. **Continue Until Zero**: Continue this process until the quotient is zero.
5. **Read the Octal Number**: The octal number is formed by reading the remainders in reverse order (from last to first).
**Example**:
Convert decimal 75 to octal.
- 75 ÷ 8 = 9 with a remainder of 3
- 9 ÷ 8 = 1 with a remainder of 1
- 1 ÷ 8 = 0 with a remainder of 1
Reading the remainders from last to first gives us **113** in octal.
### Converting Octal to Decimal
1. **Identify the Digits**: Write down the octal number, noting each digit’s place value. The rightmost digit is the least significant (8^0), the next is (8^1), and so forth.
2. **Multiply by Powers of 8**: Multiply each digit by 8 raised to the power of its position, starting from 0 on the right.
3. **Sum the Results**: Add all these products together to get the decimal equivalent.
**Example**:
Convert octal 113 to decimal.
- \(1 \times 8^2 = 1 \times 64 = 64\)
- \(1 \times 8^1 = 1 \times 8 = 8\)
- \(3 \times 8^0 = 3 \times 1 = 3\)
Now, sum them up:
64 + 8 + 3 = **75** in decimal.
### Summary of Steps
- **Decimal to Octal**: Divide by 8, record remainders, read them in reverse.
- **Octal to Decimal**: Multiply each digit by its corresponding power of 8, and sum the results.
With practice, these conversions become quicker and easier! If you have a specific number you'd like to convert, feel free to ask!
### Converting Decimal to Octal
1. **Divide by 8**: Start with the decimal number you want to convert. Divide the number by 8.
2. **Record the Remainder**: Keep track of the remainder. This will be one of the digits in the octal number. If your division results in a negative number or zero, stop here.
3. **Repeat the Division**: Take the quotient (the result of the division) and repeat the process: divide the quotient by 8, recording the new remainder.
4. **Continue Until Zero**: Continue this process until the quotient is zero.
5. **Read the Octal Number**: The octal number is formed by reading the remainders in reverse order (from last to first).
**Example**:
Convert decimal 75 to octal.
- 75 ÷ 8 = 9 with a remainder of 3
- 9 ÷ 8 = 1 with a remainder of 1
- 1 ÷ 8 = 0 with a remainder of 1
Reading the remainders from last to first gives us **113** in octal.
### Converting Octal to Decimal
1. **Identify the Digits**: Write down the octal number, noting each digit’s place value. The rightmost digit is the least significant (8^0), the next is (8^1), and so forth.
2. **Multiply by Powers of 8**: Multiply each digit by 8 raised to the power of its position, starting from 0 on the right.
3. **Sum the Results**: Add all these products together to get the decimal equivalent.
**Example**:
Convert octal 113 to decimal.
- \(1 \times 8^2 = 1 \times 64 = 64\)
- \(1 \times 8^1 = 1 \times 8 = 8\)
- \(3 \times 8^0 = 3 \times 1 = 3\)
Now, sum them up:
64 + 8 + 3 = **75** in decimal.
### Summary of Steps
- **Decimal to Octal**: Divide by 8, record remainders, read them in reverse.
- **Octal to Decimal**: Multiply each digit by its corresponding power of 8, and sum the results.
With practice, these conversions become quicker and easier! If you have a specific number you'd like to convert, feel free to ask!
Sure, converting between decimal and octal number systems is a fundamental skill in computer science and digital electronics. Here’s a detailed guide on how to perform these conversions:
### **Decimal to Octal Conversion**
To convert a decimal number to octal, follow these steps:
1. **Divide the Decimal Number**: Divide the decimal number by 8 (since octal is base 8). Record the quotient and the remainder.
2. **Record the Remainder**: The remainder will be a digit in the octal number. It will be between 0 and 7.
3. **Repeat**: Use the quotient obtained in the previous step as the new number to divide by 8. Repeat this process until the quotient is 0.
4. **Read the Octal Number**: The octal number is obtained by reading the remainders in reverse order (from the last remainder obtained to the first).
**Example**: Convert decimal 156 to octal.
1. 156 ÷ 8 = 19 (quotient), remainder = 4
2. 19 ÷ 8 = 2 (quotient), remainder = 3
3. 2 ÷ 8 = 0 (quotient), remainder = 2
Reading the remainders in reverse gives the octal number **234**.
### **Octal to Decimal Conversion**
To convert an octal number to decimal, follow these steps:
1. **Expand the Octal Number**: Write the octal number with each digit's positional value. For example, the octal number \(d_n d_{n-1} ... d_1 d_0\) can be expanded as:
\[
d_n \cdot 8^n + d_{n-1} \cdot 8^{n-1} + ... + d_1 \cdot 8^1 + d_0 \cdot 8^0
\]
2. **Calculate Each Term**: Compute each term by multiplying the digit by 8 raised to the power of its position.
3. **Sum the Terms**: Add up all the terms to get the decimal number.
**Example**: Convert octal 234 to decimal.
1. 2 × 8^2 + 3 × 8^1 + 4 × 8^0
2. = 2 × 64 + 3 × 8 + 4 × 1
3. = 128 + 24 + 4
4. = 156
### **Quick Conversion Using Programming**
If you’re using a programming language, you can often convert between decimal and octal directly using built-in functions. For example, in Python:
- **Decimal to Octal**:
```python
decimal_number = 156
octal_number = oct(decimal_number)
print(octal_number) # Output: 0o234
```
- **Octal to Decimal**:
```python
octal_number = '234'
decimal_number = int(octal_number, 8)
print(decimal_number) # Output: 156
```
These methods should help you convert numbers between decimal and octal easily.
### **Decimal to Octal Conversion**
To convert a decimal number to octal, follow these steps:
1. **Divide the Decimal Number**: Divide the decimal number by 8 (since octal is base 8). Record the quotient and the remainder.
2. **Record the Remainder**: The remainder will be a digit in the octal number. It will be between 0 and 7.
3. **Repeat**: Use the quotient obtained in the previous step as the new number to divide by 8. Repeat this process until the quotient is 0.
4. **Read the Octal Number**: The octal number is obtained by reading the remainders in reverse order (from the last remainder obtained to the first).
**Example**: Convert decimal 156 to octal.
1. 156 ÷ 8 = 19 (quotient), remainder = 4
2. 19 ÷ 8 = 2 (quotient), remainder = 3
3. 2 ÷ 8 = 0 (quotient), remainder = 2
Reading the remainders in reverse gives the octal number **234**.
### **Octal to Decimal Conversion**
To convert an octal number to decimal, follow these steps:
1. **Expand the Octal Number**: Write the octal number with each digit's positional value. For example, the octal number \(d_n d_{n-1} ... d_1 d_0\) can be expanded as:
\[
d_n \cdot 8^n + d_{n-1} \cdot 8^{n-1} + ... + d_1 \cdot 8^1 + d_0 \cdot 8^0
\]
2. **Calculate Each Term**: Compute each term by multiplying the digit by 8 raised to the power of its position.
3. **Sum the Terms**: Add up all the terms to get the decimal number.
**Example**: Convert octal 234 to decimal.
1. 2 × 8^2 + 3 × 8^1 + 4 × 8^0
2. = 2 × 64 + 3 × 8 + 4 × 1
3. = 128 + 24 + 4
4. = 156
### **Quick Conversion Using Programming**
If you’re using a programming language, you can often convert between decimal and octal directly using built-in functions. For example, in Python:
- **Decimal to Octal**:
```python
decimal_number = 156
octal_number = oct(decimal_number)
print(octal_number) # Output: 0o234
```
- **Octal to Decimal**:
```python
octal_number = '234'
decimal_number = int(octal_number, 8)
print(decimal_number) # Output: 156
```
These methods should help you convert numbers between decimal and octal easily.