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A Wallace multiplier is a hardware implementation of a binary multiplier, a digital circuit that multiplies two integers. It uses a selection of full and half adders (the Wallace tree or Wallace reduction ) to sum partial products in stages until two numbers are left.
The Dadda multiplier is a hardware binary multiplier design invented by computer scientist Luigi Dadda in 1965. [1] It uses a selection of full and half adders to sum the partial products in stages (the Dadda tree or Dadda reduction ) until two numbers are left.
It is performed by reading the binary number from left to right, doubling if the next bit is zero, and doubling and adding one if the next bit is one. [5] In the example above, 11110011, the thought process would be: "one, three, seven, fifteen, thirty, sixty, one hundred twenty-one, two hundred forty-three", the same result as that obtained above.
In a fast multiplier, the partial-product reduction process usually contributes the most to the delay, power, and area of the multiplier. [7] For speed, the "reduce partial product" stages are typically implemented as a carry-save adder composed of compressors and the "compute final product" step is implemented as a fast adder (something faster ...
In 1980, Everett L. Johnson proposed using the quarter square method in a digital multiplier. [11] To form the product of two 8-bit integers, for example, the digital device forms the sum and difference, looks both quantities up in a table of squares, takes the difference of the results, and divides by four by shifting two bits to the right.
Booth's algorithm examines adjacent pairs of bits of the 'N'-bit multiplier Y in signed two's complement representation, including an implicit bit below the least significant bit, y −1 = 0. For each bit y i, for i running from 0 to N − 1, the bits y i and y i−1 are considered.
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When working in base 2, determining the correct m at each stage is particularly easy: If the current working bit is even, then m is zero and if it's odd, then m is one. Furthermore, because each step of MultiPrecisionREDC requires knowing only the lowest bit, Montgomery multiplication can be easily combined with a carry-save adder.