Addition of Binary-Coded Decimal (BCD) Numbers
How do you add Binary-Coded Decimal (BCD) numbers?
Use the following BCD numbers and provide the correct addition:
- 0010 + 0001
- 0101 + 0011
- 0111 + 0010
- 1000 + 0001
- 00011000 + 00010001
- 01100100 + 00110011
- 01000000 + 01000111
- 10000101 + 00010011
Answer:
The correct addition of the given BCD numbers are as follows:
- 0010 + 0001 = 0011
- 0101 + 0011 = 10000
- 0111 + 0010 = 1101
- 1000 + 0001 = 1001
- 00011000 + 00010001 = 00101001
- 01100100 + 00110011 = 10010111
- 01000000 + 01000111 = 10000111
- 10000101 + 00010011 = 10011000
Detailed Explanation:
To add BCD numbers, we follow the same rules as decimal addition, but with an additional step to adjust the result if it exceeds the BCD range (0000 to 1001 for each digit).
Here's a step-by-step explanation of the first addition:
- Add the rightmost digits: 0 + 1 = 1 (no adjustment needed).
- Add the next digits to the left: 0 + 0 = 0.
- Write down the result: 0011.
Repeat this process for each pair of BCD numbers.
It's important to note that BCD numbers can only represent the digits 0 to 9 in each digit position. If the sum of two BCD digits exceeds 9, we need to adjust the result by adding 6 to it. This ensures that the result remains within the valid BCD range.
In the second addition (0101 + 0011), the sum of the rightmost digits is 1 + 1 = 10. Since this exceeds 9, we add 6 to it, resulting in 10 + 6 = 16. In BCD representation, 16 is not valid, so we adjust it by adding 6 again, giving us 16 + 6 = 22. The final result is 10000.
Continue this process for each addition, adjusting the sum as necessary.
In conclusion, adding BCD numbers involves regular addition with the additional step of adjusting the result if it exceeds the BCD range. This ensures that the final result is a valid BCD number.