Two values are stored in BCD format. They need to be added together. (a) Complete the BCD addition of 45 + 27 by filling in the table. Tens digit Units digi...
Question 1 Report
Two values are stored in BCD format. They need to be added together.
(a) Complete the BCD addition of 45 + 27 by filling in the table.
| Tens digit | Units digit | |
|---|---|---|
| First number (45) | 0100 | 0101 |
| Second number (27) | 0010 | 0111 |
| Binary sum | ||
| Adjustment needed? | ||
| Final BCD result |
[4]
(b) Explain why an adjustment of adding 0110 (6) is sometimes needed when performing BCD addition.
[2]
Answer Details
(a) BCD addition of 45 + 27:
| Tens digit | Units digit | |
|---|---|---|
| First number (45) | 0100 | 0101 |
| Second number (27) | 0010 | 0111 |
| Binary sum | 0110 | 1100 |
| Adjustment needed? | No (0110 <= 1001) | Yes (1100 > 1001) |
| Final BCD result | 0111 | 0010 |
Units: 0101 + 0111 = 1100. Since 1100 (12) exceeds 1001 (9), add the correction 0110: 1100 + 0110 = 10010. Write 0010 (2) and carry 1 to tens. [1]
Tens: 0100 + 0010 + 0001 (carry) = 0111 (7). Since 0111 does not exceed 1001, no adjustment is needed. [1]
Final BCD: 0111 0010 = 72 in denary. Check: 45 + 27 = 72. Correct. [1]
(b) The correction of adding 0110 (6) is needed because BCD only uses the 4-bit codes 0000 to 1001 (representing 0 to 9). [1] When a binary addition of two BCD digits produces a result from 1010 to 1111 (10 to 15), these are invalid in BCD. Adding 6 skips over these six unused bit patterns and generates the correct carry into the next BCD digit, keeping the result as valid BCD. [1]
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