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Check the arithmetic contract
Choose accumulator width using the complete reduction length.
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Eight-bit signed operands contribute K=4 products with no bias. The accumulator must preserve the full exact sum, including products of the most negative inputs. Choose width for the whole reduction; output scale conversion happens afterward.
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Give four operand pairs that demonstrate why a signed seventeen-bit accumulator is insufficient.
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Use (−128,−128) for every pair. Each product is 16384 and the sum is 65536, exceeding the signed seventeen-bit maximum 65535. Use the course's eighteen-bit accumulator.
Which width follows this course's conservative accumulator rule?
2W+ceil(log2 K)=16+2=18. Four minimum-input products sum to 65536, outside the signed seventeen-bit range.