How do you convert hex to decimal and vice versa?
2 Answers
Converting between hexadecimal (hex) and decimal numbers involves understanding the base systems used by each. Hexadecimal is a base-16 system, while decimal is a base-10 system. Here's a step-by-step guide to both conversions:
### Converting Hexadecimal to Decimal
Hexadecimal numbers use a base-16 system, meaning they include 16 symbols: `0-9` and `A-F`, where `A` represents 10, `B` represents 11, up to `F`, which represents 15.
**Steps to Convert Hexadecimal to Decimal:**
1. **Write Down the Hexadecimal Number:**
For example, let’s convert `2F3` to decimal.
2. **Identify the Positional Value:**
Each digit in a hexadecimal number is weighted by powers of 16, starting from the rightmost digit (which is the least significant digit).
- In `2F3`, the rightmost digit is 3 (16^0), the middle digit is F (16^1), and the leftmost digit is 2 (16^2).
3. **Convert Each Hex Digit to Decimal:**
- `3` is `3` in decimal.
- `F` is `15` in decimal.
- `2` is `2` in decimal.
4. **Calculate the Decimal Value:**
Multiply each digit by its positional value and sum the results:
\[
2F3_{16} = (2 \times 16^2) + (F \times 16^1) + (3 \times 16^0)
\]
\[
= (2 \times 256) + (15 \times 16) + (3 \times 1)
\]
\[
= 512 + 240 + 3
\]
\[
= 755
\]
So, `2F3` in hexadecimal is `755` in decimal.
### Converting Decimal to Hexadecimal
**Steps to Convert Decimal to Hexadecimal:**
1. **Write Down the Decimal Number:**
For example, let’s convert `755` to hexadecimal.
2. **Divide the Decimal Number by 16:**
Keep track of the quotient and remainder. The remainder will be the least significant digit of the hexadecimal number.
\[
755 \div 16 = 47 \text{ remainder } 7
\]
Here, 7 is the least significant digit in hexadecimal.
3. **Repeat with the Quotient:**
Take the quotient and divide by 16 again.
\[
47 \div 16 = 2 \text{ remainder } 15
\]
In hexadecimal, 15 is represented as `F`.
4. **Continue Until the Quotient is 0:**
Finally, we divide:
\[
2 \div 16 = 0 \text{ remainder } 2
\]
Here, 2 is the most significant digit.
5. **Combine the Remainders:**
The remainders collected, from last to first, give the hexadecimal number:
- Remainders collected are 2, F, 7.
- Combining them gives `2F7`.
So, `755` in decimal is `2F7` in hexadecimal.
### Summary
- **Hexadecimal to Decimal:** Multiply each hex digit by 16 raised to the power of its position (starting from 0 on the right) and sum the results.
- **Decimal to Hexadecimal:** Divide the decimal number by 16 repeatedly, recording the remainders, and read them from bottom to top to get the hexadecimal representation.
Feel free to ask if you have more questions or need additional examples!
### Converting Hexadecimal to Decimal
Hexadecimal numbers use a base-16 system, meaning they include 16 symbols: `0-9` and `A-F`, where `A` represents 10, `B` represents 11, up to `F`, which represents 15.
**Steps to Convert Hexadecimal to Decimal:**
1. **Write Down the Hexadecimal Number:**
For example, let’s convert `2F3` to decimal.
2. **Identify the Positional Value:**
Each digit in a hexadecimal number is weighted by powers of 16, starting from the rightmost digit (which is the least significant digit).
- In `2F3`, the rightmost digit is 3 (16^0), the middle digit is F (16^1), and the leftmost digit is 2 (16^2).
3. **Convert Each Hex Digit to Decimal:**
- `3` is `3` in decimal.
- `F` is `15` in decimal.
- `2` is `2` in decimal.
4. **Calculate the Decimal Value:**
Multiply each digit by its positional value and sum the results:
\[
2F3_{16} = (2 \times 16^2) + (F \times 16^1) + (3 \times 16^0)
\]
\[
= (2 \times 256) + (15 \times 16) + (3 \times 1)
\]
\[
= 512 + 240 + 3
\]
\[
= 755
\]
So, `2F3` in hexadecimal is `755` in decimal.
### Converting Decimal to Hexadecimal
**Steps to Convert Decimal to Hexadecimal:**
1. **Write Down the Decimal Number:**
For example, let’s convert `755` to hexadecimal.
2. **Divide the Decimal Number by 16:**
Keep track of the quotient and remainder. The remainder will be the least significant digit of the hexadecimal number.
\[
755 \div 16 = 47 \text{ remainder } 7
\]
Here, 7 is the least significant digit in hexadecimal.
3. **Repeat with the Quotient:**
Take the quotient and divide by 16 again.
\[
47 \div 16 = 2 \text{ remainder } 15
\]
In hexadecimal, 15 is represented as `F`.
4. **Continue Until the Quotient is 0:**
Finally, we divide:
\[
2 \div 16 = 0 \text{ remainder } 2
\]
Here, 2 is the most significant digit.
5. **Combine the Remainders:**
The remainders collected, from last to first, give the hexadecimal number:
- Remainders collected are 2, F, 7.
- Combining them gives `2F7`.
So, `755` in decimal is `2F7` in hexadecimal.
### Summary
- **Hexadecimal to Decimal:** Multiply each hex digit by 16 raised to the power of its position (starting from 0 on the right) and sum the results.
- **Decimal to Hexadecimal:** Divide the decimal number by 16 repeatedly, recording the remainders, and read them from bottom to top to get the hexadecimal representation.
Feel free to ask if you have more questions or need additional examples!
Converting between hexadecimal (hex) and decimal is a common task in computing. Here’s how you can do it for both conversions:
### Hex to Decimal
1. **Understand the Hexadecimal System**: Hexadecimal is a base-16 system. It uses digits from 0 to 9 and letters from A to F. Each digit represents a power of 16.
2. **Break Down the Hex Number**: Each digit in a hex number is multiplied by 16 raised to the power of its position (starting from 0 on the right).
For example, to convert `2F3` from hex to decimal:
- **2** is in the 16² place
- **F** (which is 15 in decimal) is in the 16¹ place
- **3** is in the 16⁰ place
Compute the decimal value:
\[
2F3_{16} = 2 \times 16^2 + F \times 16^1 + 3 \times 16^0
\]
\[
= 2 \times 256 + 15 \times 16 + 3
\]
\[
= 512 + 240 + 3
\]
\[
= 755_{10}
\]
3. **Use a Calculator or Code**: To simplify, you can use programming languages or online tools. For instance, in Python, you can use:
```python
int('2F3', 16)
```
### Decimal to Hex
1. **Understand the Process**: Decimal is a base-10 system. To convert decimal to hex, repeatedly divide the number by 16 and keep track of the remainders.
2. **Divide and Remainder**:
- Divide the decimal number by 16.
- Record the remainder (this is the least significant digit in the hex number).
- Update the number to the quotient.
- Repeat until the quotient is 0.
For example, to convert `755` from decimal to hex:
- Divide `755` by 16:
\[
755 \div 16 = 47 \text{ remainder } 3
\]
(3 is the least significant digit)
- Divide `47` by 16:
\[
47 \div 16 = 2 \text{ remainder } 15
\]
(15 in hex is F)
- Divide `2` by 16:
\[
2 \div 16 = 0 \text{ remainder } 2
\]
(2 is the most significant digit)
So, `755` in decimal is `2F3` in hex.
3. **Use a Calculator or Code**: For a quick conversion, you can use programming languages or online tools. For example, in Python:
```python
hex(755)
```
Both methods are straightforward once you get the hang of them, and using tools or code can make the process even faster.
### Hex to Decimal
1. **Understand the Hexadecimal System**: Hexadecimal is a base-16 system. It uses digits from 0 to 9 and letters from A to F. Each digit represents a power of 16.
2. **Break Down the Hex Number**: Each digit in a hex number is multiplied by 16 raised to the power of its position (starting from 0 on the right).
For example, to convert `2F3` from hex to decimal:
- **2** is in the 16² place
- **F** (which is 15 in decimal) is in the 16¹ place
- **3** is in the 16⁰ place
Compute the decimal value:
\[
2F3_{16} = 2 \times 16^2 + F \times 16^1 + 3 \times 16^0
\]
\[
= 2 \times 256 + 15 \times 16 + 3
\]
\[
= 512 + 240 + 3
\]
\[
= 755_{10}
\]
3. **Use a Calculator or Code**: To simplify, you can use programming languages or online tools. For instance, in Python, you can use:
```python
int('2F3', 16)
```
### Decimal to Hex
1. **Understand the Process**: Decimal is a base-10 system. To convert decimal to hex, repeatedly divide the number by 16 and keep track of the remainders.
2. **Divide and Remainder**:
- Divide the decimal number by 16.
- Record the remainder (this is the least significant digit in the hex number).
- Update the number to the quotient.
- Repeat until the quotient is 0.
For example, to convert `755` from decimal to hex:
- Divide `755` by 16:
\[
755 \div 16 = 47 \text{ remainder } 3
\]
(3 is the least significant digit)
- Divide `47` by 16:
\[
47 \div 16 = 2 \text{ remainder } 15
\]
(15 in hex is F)
- Divide `2` by 16:
\[
2 \div 16 = 0 \text{ remainder } 2
\]
(2 is the most significant digit)
So, `755` in decimal is `2F3` in hex.
3. **Use a Calculator or Code**: For a quick conversion, you can use programming languages or online tools. For example, in Python:
```python
hex(755)
```
Both methods are straightforward once you get the hang of them, and using tools or code can make the process even faster.