Difficulty: Easy
Correct Answer: addition
Explanation:
Introduction / Context:
BCD (binary-coded decimal) arithmetic is widely used in financial calculators, display drivers, and embedded systems that must handle decimal digits accurately. The question tests whether you know which operation underpins most BCD processing and serves as the building block for other arithmetic procedures.
Given Data / Assumptions:
Concept / Approach:
In BCD arithmetic, addition is the core primitive. Subtraction is typically performed as addition of a complement (ten's complement in decimal or BCD-corrected nine's complement plus 1). Multi-digit multiplication reduces to repeated additions of shifted partial products with BCD correction. Division uses repeated subtraction, which again relies on addition/comparison hardware and correction logic. Therefore, addition is the central operation around which BCD ALUs are designed.
Step-by-Step Solution:
1) Identify the operation most reused by others: addition is used directly and indirectly (via complements).2) Note that subtraction equals addition of a complement, implemented with adder hardware plus correction.3) Recognize that multiplication is repeated addition of partial products, digit by digit, with BCD correction.4) Division employs repeated subtraction (hence addition of complements) and comparisons.
Verification / Alternative check:
Inspect typical BCD ALU datapaths: the largest logic block is the BCD adder with correction (add 6 when a nibble exceeds 9 or when a carry is produced). Other arithmetic units reuse this block.
Why Other Options Are Wrong:
Subtraction: implemented using addition of complements.Multiplication: built from repeated additions with shifts.Division: based on repeated subtraction/comparison, again leveraging addition hardware.Iterative shifting: supports arithmetic but is not the arithmetic operation itself.
Common Pitfalls:
Assuming subtraction is separate in hardware; in many BCD ALUs it reuses the adder. Also, forgetting the BCD correction step (adding 6 when a nibble exceeds 1001) can lead to wrong decimal digits.
Final Answer:
addition
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