Multiplying signed integers

• Multiplication of two unsigned $w$-bit numbers can require as many as $2w$ bits to represent the product. So, the result is truncated.
• For $x$ and $y$ such that $TMi{n}_w\le x,y\le TMa{x}_w$,

$$x{\ast }_w^{t}y={\text{U2T}}_w((x\cdot y)\mathrm{mod}{2}^w)$$

• Here, $\text{U2T}$ implies that the result should be converted from unsigned to signed integer

Sources

• Computer Systems - A Programmer’s Perspective

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