Multiplication

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Sections

• 8-1 Multiword Multiplication
• 8-2 High-Order Half of 64-Bit Product
• 8-3 High-Order Product Signed from/to Unsigned
• 8-4 Multiplication by Constants

Problems

1. Show that for a $32\times 32\to 64$ bit multiplication, the low-order 32 bits of the product are the same whether the operands are interpreted as signed or unsigned integers.

2. Show how to modify the mulhs function, Figure 8-2, so that it calculates the low-order half of the 64-bit product, as well as the high-order half. Just show the calculation, not the parameter passing.

3. Multiplication of complex numbers is defined by

   $$(a+bi)(c+di)=ac-bd+(ad+bc)i.$$

   This can be done with only three multiplications. Let

   $$p=a(c-d),q=d(a+b),r=c(b-a).$$

   Then the product is given by

   $$p-q+(r-p-q)i,$$

   which the reader can easily verify.