A More Advanced Approach: An Unsigned Example
For example, suppose we want to multiply two unsigned eight bit integers together: a and b. We can produce eight partial products by performing eight one-bit multiplications, one for each bit in multiplicand a:
p0 = a × b = {8{a}} & b p1 = a × b = {8{a}} & b p2 = a × b = {8{a}} & b p3 = a × b = {8{a}} & b p4 = a × b = {8{a}} & b p5 = a × b = {8{a}} & b p6 = a × b = {8{a}} & b p7 = a × b = {8{a}} & bwhere {8{a}} means repeating a (the 0th bit of a) 8 times (Verilog notation).
To produce our product, we then need to add up all eight of our partial products, as shown here:
p0 p0 p0 p0 p0 p0 p0 p0 + p1 p1 p1 p1 p1 p1 p1 p1 0 + p2 p2 p2 p2 p2 p2 p2 p2 0 0 + p3 p3 p3 p3 p3 p3 p3 p3 0 0 0 + p4 p4 p4 p4 p4 p4 p4 p4 0 0 0 0 + p5 p5 p5 p5 p5 p5 p5 p5 0 0 0 0 0 + p6 p6 p6 p6 p6 p6 p6 p6 0 0 0 0 0 0 + p7 p7 p7 p7 p7 p7 p7 p7 0 0 0 0 0 0 0 ------------------------------------------------------------------------------------------- P P P P P P P P P P P P P P P PIn other words, P is produced by summing p0, p1 << 1, p2 << 2, and so forth, to produce our final unsigned 16-bit product.
Read more about this topic: Binary Multiplier
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