Question

How to convert 8 bit binary to BCD?

Answer 1

Are you looking for a specific example to convert, or do you want a general explanation of the process?

Answer 2

To convert an 8-bit binary number to Binary-Coded Decimal (BCD), you can follow these steps:

### Method 1: Using Binary-to-BCD Conversion Algorithm

1. **Start with the 8-bit binary number.** For example, let’s use `10110111` as the 8-bit binary number.

2. **Divide the 8-bit binary number into two 4-bit groups.** For `10110111`, the groups are `1011` and `0111`.

3. **Convert each 4-bit group to its decimal equivalent.**
   - `1011` in binary is `11` in decimal.
   - `0111` in binary is `7` in decimal.

4. **Convert these decimal values into BCD format.** BCD represents each decimal digit with a 4-bit binary value:
   - Decimal `11` is not valid in BCD as BCD only represents decimal digits 0-9.
   - Decimal `7` in BCD is `0111`.

   For our purpose, assuming the number is correctly represented, if you need to handle numbers exceeding 9 in BCD, you'd need to break it down further into two decimal digits.

5. **Combine the BCD representations if necessary.**

   In this case:
   - For `10110111` (which is `183` in decimal), convert `18` and `3` separately to BCD:
     - Decimal `18` in BCD is `0001 1000` (1 and 8).
     - Decimal `3` in BCD is `0000 0011` (3).

   So the 8-bit binary number `10110111` would be represented as `0001 1000 0000 0011` in BCD.

### Method 2: Using a Conversion Table (for quick conversion)

1. **Create a table mapping binary numbers to their BCD equivalents.**

   For instance:
   ```
   Binary | Decimal | BCD
   -------|---------|-----
   0000   | 0       | 0000
   0001   | 1       | 0001
   0010   | 2       | 0010
   0011   | 3       | 0011
   0100   | 4       | 0100
   0101   | 5       | 0101
   0110   | 6       | 0110
   0111   | 7       | 0111
   1000   | 8       | 1000
   1001   | 9       | 1001
   ```

2. **Look up the decimal equivalent of your 8-bit binary number.** For `10110111`, which is `183` in decimal.

3. **Convert the decimal number to BCD.** For `183`, it is `0001 1000 0011`.

### Summary

- Split the binary number into 4-bit segments if it is more than 4 bits long.
- Convert each segment to its decimal equivalent.
- Represent each decimal digit in 4-bit BCD format.
- Combine the BCD representations if necessary.

If you have specific binary numbers or need more detailed examples, let me know!