Search results
Results from the WOW.Com Content Network
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 ...
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.
Brickell [3] has published a similar algorithm that requires greater complexity in the electronics for each digit of the accumulator.. Montgomery multiplication is an alternative algorithm which processes the multiplier "backwards" (least significant digit first) and uses the least significant digit of the accumulator to control whether or not the modulus should be added.
Multiply each bit of one of the arguments, by each bit of the other. Reduce the number of partial products to two by layers of full and half adders. Group the wires in two numbers, and add them with a conventional adder. [3] Compared to naively adding partial products with regular adders, the benefit of the Wallace tree is its faster speed.
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.
The advantage over 8-bit or 16-bit integers is that the increased dynamic range allows for more detail to be preserved in highlights and shadows for images, and avoids gamma correction. The advantage over 32-bit single-precision floating point is that it requires half the storage and bandwidth (at the expense of precision and range). [5]
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.
The algorithm may use as little as p + 2 words of storage (plus a carry bit). As an example, let B = 10, N = 997, and R = 1000. Suppose that a = 314 and b = 271. The Montgomery representations of a and b are 314000 mod 997 = 942 and 271000 mod 997 = 813. Compute 942 ⋅ 813 = 765846. The initial input T to MultiPrecisionREDC will be [6, 4, 8, 5 ...