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LUT-Based Matrix Multiplier Circuit Using Pigeonhole Principle
Published in Hafiz Md. Hasan Babu, VLSI Circuits and Embedded Systems, 2023
For the multiplication of an n-bit multiplicand with an m-bit multiplier, m partial products are generated and product formed is n+m bits long. Here about five different types of multipliers are discussed which are as follows: Booth multiplier.Combinational multiplier.Wallace tree multiplier.Array multiplier.Sequential multiplier.
Arithmetic and Logic Unit Organisation
Published in Pranabananda Chakraborty, Computer Organisation and Architecture, 2020
A multiplier circuit can be implemented using a multistage CSA circuit (already described earlier). This circuit is popularly known as a Wallace tree after the name of its inventor (Wallace 1964). The inputs to the adder tree are n terms of the form Mi = xiY 2k. Here, Mirepresents the multiplicand Y multiplied by the ith multiplier bit weighted by the appropriate power of 2. Suppose Mi is 2n-bit long, and that a full double-length product is required, the desired product P is ∑i=0n−1Mi. This sum is computed by the CSA tree that produces a 2n-bit sum and a 2n-bit carry word. The final carry assimilation is then usually performed by a fast adder, a CLA, for instance, with normal internal carry propagation.
Structured Digital Design
Published in Louis Scheffer, Luciano Lavagno, Grant Martin, EDA for IC Implementation, Circuit Design, and Process Technology, 2018
Improvement in speed can be achieved through rearranging the CSAs such that the longest path is reduced from N to log N. An example is the so-called Wallace tree multiplier illustrated in Figure 7.4 [1]. The notation Abi in the figure means a partial product vector. The big disadvantage of a Wallace tree multiplier is the loss of regularity in the layout. Other techniques like Booth encoding can also be used to improve the performance of the multiplier [1].
FPGA implementation of high performance digital FIR filter design using a hybrid adder and multiplier
Published in International Journal of Electronics, 2023
The array multiplier was designed using modified full adder-based multiplexer. This multiplier consumed less power. In order to increase the speed of the multiplication, the Wallace tree multiplier was introduced. In proposed tree multiplier, partial product accumulation speed was increased because the carry save adder was used instead of RCA (Hussain et al., 2019).
FPGA implementation of proficient Vedic multiplier architecture using hybrid carry select adder
Published in International Journal of Electronics, 2023
To reduce the delay of multiplication, Wallace tree multiplier is introduced. The advantage of Wallace tree multiplier as compared to array multiplier is the minimisation of delay, but it increases the memory requirement and power consumption.