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- Wallace_tree abstract "A Wallace tree is an efficient hardware implementation of a digital circuit that multiplies two integers, devised by an Australian Computer Scientist Chris Wallace in 1964.The Wallace tree has three steps: Multiply (that is - AND) each bit of one of the arguments, by each bit of the other, yielding results. Depending on position of the multiplied bits, the wires carry different weights, for example wire of bit carrying result of is 32 (see explanation of weights below). 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.The second phase works as follows. As long as there are three or more wires with the same weight add a following layer: Take any three wires with the same weights and input them into a full adder. The result will be an output wire of the same weight and an output wire with a higher weight for each three input wires. If there are two wires of the same weight left, input them into a half adder. If there is just one wire left, connect it to the next layer.The benefit of the Wallace tree is that there are only reduction layers, and each layer has propagation delay. As making the partial products is and the final addition is , the multiplication is only , not much slower than addition (however, much more expensive in the gate count). Naively adding partial products with regular adders would require time. From a complexity theoretic perspective, the Wallace tree algorithm puts multiplication in the class NC1.These computations only consider gate delays and don't deal with wire delays, which can also be very substantial.The Wallace tree can be also represented by a tree of 3/2 or 4/2 adders.It is sometimes combined with Booth encoding.".
- Wallace_tree thumbnail Hindu_lattice_2.svg?width=300.
- Wallace_tree wikiPageExternalLink 655-vhdl-component-wallace-tree-multiplier-generic.html.
- Wallace_tree wikiPageID "4180990".
- Wallace_tree wikiPageRevisionID "544546926".
- Wallace_tree hasPhotoCollection Wallace_tree.
- Wallace_tree subject Category:Computer_arithmetic.
- Wallace_tree subject Category:Digital_circuits.
- Wallace_tree type Artifact100021939.
- Wallace_tree type Circuit103033362.
- Wallace_tree type Device103183080.
- Wallace_tree type DigitalCircuits.
- Wallace_tree type ElectricalDevice103269401.
- Wallace_tree type Instrumentality103575240.
- Wallace_tree type Object100002684.
- Wallace_tree type PhysicalEntity100001930.
- Wallace_tree type Whole100003553.
- Wallace_tree comment "A Wallace tree is an efficient hardware implementation of a digital circuit that multiplies two integers, devised by an Australian Computer Scientist Chris Wallace in 1964.The Wallace tree has three steps: Multiply (that is - AND) each bit of one of the arguments, by each bit of the other, yielding results. Depending on position of the multiplied bits, the wires carry different weights, for example wire of bit carrying result of is 32 (see explanation of weights below).".
- Wallace_tree label "Wallace tree".
- Wallace_tree label "Wallace-Tree-Multiplizierer".
- Wallace_tree sameAs Wallace-Tree-Multiplizierer.
- Wallace_tree sameAs m.0bnkj5.
- Wallace_tree sameAs Q2542512.
- Wallace_tree sameAs Q2542512.
- Wallace_tree sameAs Wallace_tree.
- Wallace_tree wasDerivedFrom Wallace_tree?oldid=544546926.
- Wallace_tree depiction Hindu_lattice_2.svg.
- Wallace_tree isPrimaryTopicOf Wallace_tree.
