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Radix-8 Design Alternatives of Fast Two Operands Interleaved Multiplication with Enhanced Architecture Cover

Radix-8 Design Alternatives of Fast Two Operands Interleaved Multiplication with Enhanced Architecture

Open Access
|Oct 2019

Figures & Tables

Figure 1.

Carry save Adder: (a) Top View Design (b) Internal Architecture

Figure 2.

Delay-Area analysis of CSA vs CLA implementations (8–64 bit)

Figure 3.

Kogge Stone Adder: (a) Top View Design of KSA (c) KSA Stages (c) Group generation and propagation

Figure 4.

Dot notation of Multi-operand addition for multiplication and inner-product computation

Figure 5.

Multi-operand addition for 10 operands.

Figure 6.

Aligning Partial Products.

Figure 7.

The complete design of8- Bit Comparatorincluding Pre- Encoding circuit and Comp circuit

Figure 8.

Design of Radix-8 Booth 32-bit multiplier

Figure 9.

State machine diagram for 32-bit Booth multiplier.

Figure 10.

Design of 64-bit CSA Based Radix-8 Booth, Wallace Tree Karatsuba multiplier.

Figure 11.

Graphical approaches to demonstrate the carry error (the mid-carry problem), here we have two cases: Case I- ps1+ pc1 = might result in carry, result = 65-bit (wrong). Carry must be discarded and Case II- ps1+ ps2 = might result in carry, result = 65-bit (correct). Carry must be considered.

Figure 12.

Design of 64-bit: 64-bit CSA Based Radix-8 Booth, KSA Based Karatsuba multiplier.

Figure 13.

Karatsuba multiplication based on CSA and comparator.

Figure 14.

Design of CSA based Radix-8 Booth 64-bit multiplier.

Figure 15.

(a) Design Architecture of WCBM (a) Top Level DiagramWCBM (C) FSM Diagram for WCBM.

Figure 16.

Sample run example of WCBM process of two 64-bit numbers

Figure 17.

Waveform sample of the proposed WCBM data delay

COMPARISON BETWEEN DESIGN II & DESIGN III_

Design Solutions #Delay (gate delay)% OptimizationArea (# of gates)% Optimization
Solution I: using KSA Adder.23+15%6130 
Solution II: using Comparator unit.27 3712+50%

RADIX-8 BOOTH ENCODING_

Inputs (bits of M-bit multiplier)Partial Product
xi+2 xi+1 xi xi−1 PPRi
00000
0001A
0010A
00112A
01002A
01013A
01103A
01114A
1000-4A
1001-3A
1010-3A
1011-2A
1100-2A
1101-A
1110-A
11110
Language: English
Page range: 15 - 27
Published on: Oct 8, 2019
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2019 Mohammad M. Asad, Ibrahim Marouf, Qasem Abu Al-Haija, published by Xi’an Technological University
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.