Question

How we can convert from hexadecimal to binary and vice versa?

Answer 1

Converting between hexadecimal (base-16) and binary (base-2) is a common task in computing and digital electronics. Here's a detailed explanation of how to perform these conversions in both directions:

### Converting from Hexadecimal to Binary

1. **Understand the Basics**: Hexadecimal is a base-16 system, meaning it uses 16 symbols: 0-9 and A-F. Each hexadecimal digit corresponds to a 4-bit binary sequence. For example:
   - Hexadecimal 0 = Binary 0000
   - Hexadecimal 1 = Binary 0001
   - Hexadecimal 2 = Binary 0010
   - Hexadecimal 3 = Binary 0011
   - ...
   - Hexadecimal A = Binary 1010
   - Hexadecimal F = Binary 1111

2. **Convert Each Hex Digit to Binary**:
   - Take each hexadecimal digit and convert it to its 4-bit binary equivalent.
   - For example, to convert the hexadecimal number `3F`:
     - Hex `3` converts to Binary `0011`
     - Hex `F` converts to Binary `1111`
   - Combine these binary groups to get the full binary representation: `0011 1111`

3. **Example**:
   - Convert `2A3` to binary:
     - Hex `2` = Binary `0010`
     - Hex `A` = Binary `1010`
     - Hex `3` = Binary `0011`
   - The binary representation is `0010 1010 0011`.

### Converting from Binary to Hexadecimal

1. **Group Binary Digits**: Binary is a base-2 system, and each hexadecimal digit represents 4 binary digits. Therefore, group the binary digits into sets of four, starting from the right. If there are fewer than 4 digits on the left, pad with zeros.

2. **Convert Each 4-Bit Binary Group to Hex**:
   - Convert each 4-bit binary group to its hexadecimal equivalent.
   - For example, to convert the binary number `11010110`:
     - Group into `1101` and `0110`
     - Binary `1101` converts to Hex `D`
     - Binary `0110` converts to Hex `6`
   - Combine these hexadecimal digits: `D6`

3. **Example**:
   - Convert `101101011` to hexadecimal:
     - Pad to get a complete group of 4: `0101 1010 11`
     - Group into `0001` `0101` `1010` `0011`
     - Binary `0001` = Hex `1`
     - Binary `0101` = Hex `5`
     - Binary `1010` = Hex `A`
     - Binary `0011` = Hex `3`
   - The hexadecimal representation is `15A3`.

### Summary

- **Hexadecimal to Binary**: Convert each hex digit to a 4-bit binary sequence.
- **Binary to Hexadecimal**: Group binary digits into sets of four, then convert each group to a hex digit.

These conversions are straightforward once you get familiar with the basic representations. For quick conversions, you can use conversion tables or calculators, but understanding the underlying process is useful for better grasping how these systems work.

Answer 2

To convert between hexadecimal and binary, you can use the following methods:

### Hexadecimal to Binary

1. **Convert Each Hex Digit to Binary:**
   - Each hexadecimal digit can be represented by a 4-bit binary number.
   - Use the following conversions:
     - 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

   - Example: To convert hexadecimal `2F` to binary:
     - `2` → 0010
     - `F` → 1111
     - Combine them: `0010 1111`

### Binary to Hexadecimal

1. **Group Binary Digits into Sets of 4:**
   - Starting from the right, group the binary digits into sets of 4.
   - If the number of binary digits isn't a multiple of 4, pad the leftmost group with zeros.

2. **Convert Each Binary Group to Hexadecimal:**
   - Use the same conversions as above to convert each 4-bit group to a hexadecimal digit.

   - Example: To convert binary `11010111` to hexadecimal:
     - Group into sets of 4: `1101 0111`
     - `1101` → D
     - `0111` → 7
     - Combine them: `D7`

By following these methods, you can easily convert between hexadecimal and binary representations.