Question

How to convert hexadecimal to binary and vice versa?

Answer 1

Converting between hexadecimal and binary is straightforward, as each hexadecimal digit corresponds to a 4-bit binary sequence. Here’s how you can do it both ways:

### Hexadecimal to Binary
1. **Write down the hexadecimal number.**
2. **Convert each hex digit to its 4-bit binary equivalent.** Here’s a reference for hex to binary conversion:

   | Hex | Binary   |
   |-----|----------|
   | 0   | 0000     |
   | 1   | 0001     |
   | 2   | 0010     |
   | 3   | 0011     |
   | 4   | 0100     |
   | 5   | 0101     |
   | 6   | 0110     |
   | 7   | 0111     |
   | 8   | 1000     |
   | 9   | 1001     |
   | A   | 1010     |
   | B   | 1011     |
   | C   | 1100     |
   | D   | 1101     |
   | E   | 1110     |
   | F   | 1111     |

3. **Concatenate the binary sequences.** For example, to convert `2F` to binary:
   - `2` → `0010`
   - `F` → `1111`
   - Result: `00101111`

### Binary to Hexadecimal
1. **Write down the binary number.**
2. **Group the binary digits into sets of four, starting from the right.** If the leftmost group has less than four digits, you can pad it with leading zeros.
3. **Convert each group to its hexadecimal equivalent.** Use the reference table above for conversion.
4. **Concatenate the hex digits.** For example, to convert `11011100` to hexadecimal:
   - Group: `1101 1100`
   - `1101` → `D`
   - `1100` → `C`
   - Result: `DC`

### Example Conversions
- **Hex to Binary:** `1A3`
  - `1` → `0001`
  - `A` → `1010`
  - `3` → `0011`
  - Result: `000110100011`

- **Binary to Hex:** `10110111`
  - Group: `1011 0111`
  - `1011` → `B`
  - `0111` → `7`
  - Result: `B7`

These steps should help you convert between hexadecimal and binary easily!

Answer 2

Converting between hexadecimal and binary is pretty straightforward once you get the hang of it. Here’s a simple guide for both conversions:

### Hexadecimal to Binary

1. **Understand the Basics:**
   - Each hexadecimal digit corresponds to a 4-bit binary number.
   - Hexadecimal digits range from 0-9 and A-F, where A=10, B=11, C=12, D=13, E=14, F=15.

2. **Convert Each Hex Digit to Binary:**
   - **Hex 0-9:** Convert directly to a 4-bit binary equivalent.
     - For example, 0 in hex is 0000 in binary, and 9 in hex is 1001 in binary.
   - **Hex A-F:** Convert by finding their binary equivalents.
     - For example, A in hex is 1010 in binary, and F in hex is 1111 in binary.

3. **Combine the Results:**
   - Write down the binary equivalent for each hex digit in sequence.

   **Example:**
   - Convert hex `2F` to binary:
     - `2` in hex = `0010` in binary
     - `F` in hex = `1111` in binary
     - So, `2F` in hex = `00101111` in binary.

### Binary to Hexadecimal

1. **Group the Binary Digits:**
   - Group the binary digits into sets of 4, starting from the right. If the number of digits isn’t a multiple of 4, pad with leading zeros.

2. **Convert Each 4-bit Group to Hex:**
   - Convert each 4-bit binary group to its hexadecimal equivalent.
     - For example, `1010` in binary = `A` in hex.

3. **Combine the Results:**
   - Write down the hex digits in sequence.

   **Example:**
   - Convert binary `11011010` to hex:
     - Group into 4-bit groups: `1101 1010`
     - Convert each group: `1101` = `D` and `1010` = `A`
     - So, `11011010` in binary = `DA` in hex.

Feel free to ask if you have a specific number you need help with!