# 8.2.4 Binary Multiplication | Summary and Q&A

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July 12, 2019
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8.2.4 Binary Multiplication

## TL;DR

Multipliers in arithmetic and logic units are slow and large, but by making tradeoffs, they can be made smaller or faster.

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### Q: Why is the multiplier circuit one of the slowest and largest circuits?

The multiplier circuit requires the computation of multiple partial products and their subsequent addition, which increases the latency and hardware requirements.

### Q: How does the multiplication process work?

The multiplication process involves multiplying each digit of the multiplier with each digit of the multiplicand, and shifting the partial products to the left to reflect the increasing weight of the multiplier digits.

### Q: What are the challenges when dealing with two's complement operands in multiplication?

With two's complement operands, the high-order bit has negative weight, requiring sign-extension of the partial products. Additional computations are needed to handle the subtraction of the last partial product.

### Q: How can the hardware costs be reduced in multiplier circuits?

Hardware costs can be reduced by making tradeoffs, such as using NAND gates instead of AND gates for necessary complements and optimizing the circuit layout.

## Summary & Key Takeaways

• Multipliers are one of the largest and slowest circuits in arithmetic and logic units.

• The process of multiplication involves breaking down the operands into digits and using multiplication tables to calculate the partial products.

• The multiplication circuit requires AND gates for forming the partial products and adder modules for adding them together.