Exam-style question
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Calculate 1101₂ × 101₂ using binary multiplication. Show the partial products and the final answer.
Model answer
What a good answer should say
- 1101₂ × 101₂ = 1000001₂.
Explanation
Why this works
The rightmost multiplier bit gives 1101₂. The middle multiplier bit is 0, so its partial product is 00000₂.
The leftmost multiplier bit is 1, so 1101₂ is shifted two places, giving 110100₂. Adding the partial products gives 0001101₂ + 110100₂ = 1000001₂.
As a check, 13 × 5 = 65, which is 1000001₂.
Common mistake
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