Multi-digit decimal addition using BCD adders: When several-digit decimal numbers are added using BCD, ________.
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Aa separated BCD adder is required for each digit position
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Bthe BCD adders must have the carry-outs grounded
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Cthe BCD digits must be grouped in twos
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Dfull adders are also used
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Ethe low digit alone needs a BCD adder
Answer
Correct Answer: a separated BCD adder is required for each digit position
Explanation
Introduction / Context:Binary-coded decimal (BCD) represents each decimal digit with a 4-bit nibble. Adding multi-digit decimal values requires per-digit correction (adding 0110 when a nibble exceeds 1001 or generates a carry) and proper carry propagation to higher digits.
Given Data / Assumptions:
- Each decimal digit = 4-bit BCD nibble.
- Nibble sums may need +0110 correction.
- Digit-to-digit carry must propagate.
Concept / Approach:Build the adder as a cascade: one BCD adder stage per decimal digit (ones, tens, hundreds, …). Each stage performs binary add of the two BCD nibbles plus Cin, then conditionally adds 0110 if needed, outputting a corrected BCD nibble and a carry to the next stage.
Step-by-Step Solution:
Instantiate a BCD adder for each digit.Connect Cout of lower digit to Cin of next digit.Apply 0110 correction per stage when nibble > 1001 or carry=1.Verification / Alternative check:Worked examples of multi-digit BCD sums show each digit independently corrected with carries chained upward.
Why Other Options Are Wrong:
Grounding carry-outs: Breaks multi-digit propagation.Grouping in twos / full adders: Not sufficient; need BCD correction logic per digit.Only low digit BCD: All digits require correction capability.Common Pitfalls:Forgetting that a nibble 1010–1111 is invalid BCD and must be corrected.
Final Answer:a separated BCD adder is required for each digit position