Question

How to convert binary to hexadecimal and vice versa?

Answer 1

To convert between binary and hexadecimal, you can follow these steps:

### Binary to Hexadecimal:

1. **Group the Binary Digits**: Starting from the right, group the binary digits into sets of four. If necessary, add leading zeros to make a complete group of four.
   - Example: `10110110` becomes `1011 0110`.

2. **Convert Each Group**: Convert each 4-bit binary group to its hexadecimal equivalent.
   - `1011` = B
   - `0110` = 6

3. **Combine the Hexadecimal Digits**: Write the hexadecimal digits together.
   - So, `10110110` in binary = `B6` in hexadecimal.

### Hexadecimal to Binary:

1. **Convert Each Hexadecimal Digit**: Convert each hexadecimal digit to its 4-bit binary equivalent.
   - `B` = `1011`
   - `6` = `0110`

2. **Combine the Binary Digits**: Write the binary digits together.
   - So, `B6` in hexadecimal = `10110110` in binary.

### Example:

- **Binary to Hexadecimal**: `110101101001` → Group: `1101 0110 01` → Add leading zeros: `0011 0101 1010 0001` → Convert: `3 D A 1`.
- **Hexadecimal to Binary**: `3DA1` → Convert: `0011 1101 1010 0001`.

Feel free to ask if you need more examples or details!

Answer 2

Converting between binary and hexadecimal is straightforward once you understand the relationship between the two number systems. Here's a step-by-step guide:

### Converting Binary to Hexadecimal

1. **Group the binary digits**: Split the binary number into groups of four digits, starting from the right. Add leading zeros if necessary to make a complete group of four.

   Example: Binary number `11010110` becomes `1101 0110`.

2. **Convert each group to hexadecimal**: Convert each 4-bit binary group to its hexadecimal equivalent using a conversion table or direct calculation.

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

   Applying this to our example:
   - `1101` = `D`
   - `0110` = `6`

   So, `11010110` in binary converts to `D6` in hexadecimal.

### Converting Hexadecimal to Binary

1. **Convert each hexadecimal digit to binary**: Use a conversion table to change each hex digit into its 4-bit binary equivalent.

   Example: Hexadecimal `A3` becomes:

   - `A` = `1010`
   - `3` = `0011`

   So, `A3` in hexadecimal converts to `10100011` in binary.

2. **Combine the binary groups**: Simply concatenate the binary representations of each hex digit.

### Summary

- **Binary to Hexadecimal**: Group binary digits into sets of four, then convert each group to its hex equivalent.
- **Hexadecimal to Binary**: Convert each hex digit to its 4-bit binary equivalent and concatenate them.

Feel free to ask if you need more examples or clarifications!