BCD adder count: How many BCD adder stages are needed to add the decimal numbers 973₁₀ and 39₁₀?

Introduction / Context:
Binary-coded decimal (BCD) adders operate on digits (0–9) encoded in 4 bits each. Multi-digit decimal addition uses one BCD adder per decimal digit, plus carry correction logic for sums ≥ 10.

Given Data / Assumptions:

• Numbers: 973 and 39 (both base-10).
• BCD addition aligns digits by place value.
• Each BCD adder handles one decimal digit.

Concept / Approach:
Write the smaller addend with leading zeros so both numbers have equal digits. The number of digits equals the number of required BCD adder stages, connected least significant to most significant with carry propagation.

Step-by-Step Solution:
Rewrite 39 as 039 to align with 973.Digits: hundreds (9 vs 0), tens (7 vs 3), ones (3 vs 9).Therefore, three BCD digit positions ⇒ three BCD adder stages.

Verification / Alternative check:
Perform decimal addition: 973 + 39 = 1,012. Even though the result has four digits, the hardware still uses three cascaded BCD adders for the three input columns; a carry out from the most significant digit produces the extra thousand.

Why Other Options Are Wrong:
2: Would handle only two least significant digits, losing the hundreds column.4, 5, 6: Exceed the number of aligned input digits.

Common Pitfalls:
Confusing the number of digits in the result with the number of digit adders required; hardware sizing follows input width, not the potential carry out.

Final Answer:
3