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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 sum-output from the second half adder is the final sum output of the full adder and the output from the OR gate is the final carry output (). The critical path of a full adder runs through both XOR gates and ends at the sum bit . Assumed that an XOR gate takes 1 delays to complete, the delay imposed by the critical path of a full adder is ...
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 than ripple-carry). Many fast multipliers use full adders as compressors ("3:2 compressors") implemented in static CMOS.
A carry-skip adder [nb 1] (also known as a carry-bypass adder) is an adder implementation that improves on the delay of a ripple-carry adder with little effort compared to other adders. The improvement of the worst-case delay is achieved by using several carry-skip adders to form a block-carry-skip adder.
A carry-save adder [1] [2] [nb 1] is a type of digital adder, used to efficiently compute the sum of three or more binary numbers. It differs from other digital adders in that it outputs two (or more) numbers, and the answer of the original summation can be achieved by adding these outputs together.
An example of a 4-bit Kogge–Stone adder is shown in the diagram. Each vertical stage produces a "propagate" and a "generate" bit, as shown. The culminating generate bits (the carries) are produced in the last stage (vertically), and these bits are XOR'd with the initial propagate after the input (the red boxes) to produce the sum bits. E.g., the first (least-significant) sum bit is ...
A partial full adder, with propagate and generate outputs. Logic gate implementation of a 4-bit carry lookahead adder. A block diagram of a 4-bit carry lookahead adder. For each bit in a binary sequence to be added, the carry-lookahead logic will determine whether that bit pair will generate a carry or propagate a carry.
In general, a logic block consists of a few logical cells. A typical cell consists of a 4-input LUT, a full adder (FA) and a D-type flip-flop. The LUT might be split into two 3-input LUTs. In normal mode those are combined into a 4-input LUT through the first multiplexer (mux). In arithmetic mode, their outputs are fed to the adder. The ...