To implement a 9 x 9 complex multiplier, 2 Math blocks and an additional
2's complement logic (in the fabric) are required. The 2's complement logic in the fabric
is needed for negating the Q input, as shown in Figure 3-12, and
this logic consumes minimal fabric resources.
For two complex numbers, X + jY and P + jQ, the complex multiplication is:
Multiplication result = real part + imaginary part = (PX – QY) + j (PY + QX).
The real part (PX - QY) requires -Q for the multiplication result. In 2's complement arithmetic this value can be computed using the 1's complement of Q and adding the Y using the C input (-Q = ~Q + 1).
Real part = P x X + (~Q) x Y + Y.Figure 3-12. 9-Bit Complex Multiplication Using DOTP Mode
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