Introduction:
Binary-coded decimal (BCD) represents each decimal digit with a 4-bit code from 0000 to 1001. When adding BCD digits, binary sums may land in invalid codes (1010 to 1111). BCD correction fixes such cases by adding a specific constant to force a carry and bring the low nibble back into a valid range.
Given Data / Assumptions:
- BCD digit codes: valid 0000–1001, invalid 1010–1111.
- We are discussing single-digit correction logic.
- Typical hardware uses adders plus correction/adjust logic.
Concept / Approach:
The standard correction is to add 6 decimal (0110₂) when the 4-bit sum exceeds 9 (i.e., is invalid) or when a carry is generated from the lower nibble. Adding 0110 normalizes the nibble and properly propagates a carry to the next BCD digit, maintaining decimal correctness.
Step-by-Step Solution:
Step 1: Perform 4-bit binary addition of two BCD digits and any carry-in.Step 2: If the nibble > 1001 (decimal > 9) or a carry occurred, add 0110.Step 3: The addition of 0110 forces a valid BCD result and produces/adjusts the carry to the next higher digit.
Verification / Alternative check:
Example: 1001 (9) + 0101 (5) = 1110 (14, invalid). Add 0110 → 1 0100; low nibble 0100 (4) with a carry to the tens digit, giving 14 decimal overall.
Why Other Options Are Wrong:
010101: Six bits; not a single-nibble correction and not standard BCD fix.0U812: Not a binary constant; invalid token.100110: Six bits again; does not match the canonical nibble correction.
Common Pitfalls:
Forgetting to add 0110 when the nibble is 1010–1111.Confusing hexadecimal adjustment (DAA) with BCD nibble correction rules.
Final Answer:
0110
Discussion & Comments