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研究生: 廖美貞
Irene M.-J. Liao
論文名稱: 高效能布斯加密法瓦利氏樹結構乘法器之進位選擇加法器的最佳化技術
A Carry-Select-Adder Optimization Technique for High-Performance Booth-Encoded Wallace-Tree Multipliers
指導教授: 吳中浩
Allen C.-H. Wu
口試委員:
學位類別: 碩士
Master
系所名稱: 電機資訊學院 - 資訊工程學系
Computer Science
論文出版年: 2001
畢業學年度: 89
語文別: 英文
論文頁數: 56
中文關鍵詞: 進位加法選擇器高效能乘法器
外文關鍵詞: carry-select adder, high-performance multupliers
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  • 在這篇論文中, 我們提出了兩個在高效能布斯加密法瓦利氏樹乘法器(Booth-Encoded Wallace-Tree Multiplier)中進位選擇加法器(carry-select-adder)分配演算法, 一為branch-and-bound方法, 一為heuristic方法; 由於資料進入進位選擇加法器時間的不同, 我們將進位選擇加法器分為若干個加法器區塊, 以對乘法器的效能作最佳化. 我們使用我們所做的乘法器產生器產生了15個乘法器, 從實驗數據中可得知, 在不到1%的面積增加下, 可以有約9.2%的效能進步.


    In this thesis, we present two carry-select adder partitioning algorithms for high-performance Booth-encoded Wallace-tree multipliers. By taking various data arrival times into account, we propose a branch-and-bound algorithm and a heuristic algorithm to partition an n-bit carry-select adder into a number of adder blocks such that the overall delay of the design is minimized. The experimental results show that our proposed algorithm can achieve on an average 9.1% delay reduction with less than 1% of area overhead on 15 multipliers ranges from 16X16-bit to 64X64-bit.

    Contents Abstract Contents List of Figures List of Tables Chapter 1 : Introduction Chapter 2 : Related Work Chapter 3 : Overview of the Booth-Encoded Wallace Tree Multiplier 3.1 Multiplier Architecture 3.2 Partial Product Generator 3.2.1 A Modified Radix-4 Booth’s Algorithm 3.2.2 Sign-Pre-Calculation 3.3 The Partial-Product-Reduction Tree Structure 3.4 Carry-Select Adder Chapter 4 : Problem Description 4.1 Delay Effect on Carry-Select Adder Partitioning 4.2 Problem Definition Chapter 5 : The Carry-Select Adder Partitioning Algorithm 5.1 Branch-and-Bound Method 5.2 Heuristic Algorithm Chapter 6 : Implementation and Experimental Results 6.1 Experiments on Branch-and-Bound Algorithm v.s. Heuristic Algorithm 6.2 Experiments on Our Proposed Heuristic Algorithm v.s. the CSA Partitioning Method Proposed by [6] 6.3 Experiments on the Multipliers Generated by Our Multiplier Generator Chapter 7 : Conclusions and Future Work References

    [1] Junhyung Um, Taewhan Kim, C. L. Liu, “Optimal Allocation of Carry-Save-Adders in Arithmetic Optimization”, ICCAD, pp.410~413 1999.
    [2] Junhyung Um, Taewhan Kim, C. L. Liu, “A Fine-Grained Arithmetic Optimization Technique for High-Performance/Low-Power Data Path Synthesis”, DAC, P92-P97, 2000.
    [3] Oklobdzija, V.G.; Villeger, D.; Liu, S.S., “A method for speed optimized partial product reduction and generation of fast parallel multipliers using an algorithmic approach” IEEE Transactions on Computers, Vol. 45 3, March 1996 , P294-P306.
    [4] Martel, C., Oklobdzija, V., Ravi, R., Stelling, P.F., ”Design strategies for optimal multiplier circuits”, Proceedings of the 12th Symposium on Computer Arithmetic, 1996, P42-P49.
    [5] Meier, P.C.H.; Rutenbar, R.A.; Carley, L.R., “Exploring multiplier architecture and layout for low power”, Proceedings of the IEEE on Custom Integrated Circuits Conference, pp.513-516, 1996.
    [6] Jalil Fadavi-Ardekani, Senior Member, IEEE, ”M*N Booth Encoded Multiplier Generator Using Optimized Wallace Trees” IEEE Transaction on VLSI System, Vol. 12, June 1993, P120-P125.
    [7] Stelling, P.F., Oklobdzija, V., “Design strategies for the final adder in a parallel multiplier” Conference Record of the 29th Asilomar Conference on Signals, Systems and Computers, Vol. 1, 1996, P591-P595.
    [8] Stelling, P.F., Oklobdzija, V.G., “Implementing multiply-accumulate operation in multiplication time”, 13th IEEE Symposium on Computer Arithmetic, 1997, P99-P106.
    [9] Stelling, P.F., Martel, C.U., Oklobdzija, V.G., Ravi, R., “Optimal circuits for parallel multipliers”, IEEE Transactions on Computers, Vol. 47 3, March 1998, P273-P285.
    [10] Wen-Chang Yeh; Chein-Wei Jen , “High-speed Booth encoded parallel multiplier design” IEEE Transactions on Computers, Vol. 49 7, P692 -P701, July 2000.
    [11] Kolagotla, R.K., Srinivas, H.R., Burns, G.F., “VLSI implementation of a 200-MHz 16/spl times/16 left-to-right carry-free multiplier in 0.35 /spl mu/m CMOS technology for next-generation DSPs”, Proceedings of the IEEE Custom Integrated Circuits Conference, 1997, P469-P472 vol. 1, No. 2, June 1993.
    [12] C. S. Wallace “A suggestion for a Fast Multiplier”, IEEE Transaction on Computers, Vol. EC-13, P14-P17, 1964.
    [13] A.D. Booth, “A Signed Binary Multiplication Technique”, Quart. J. Math., vol. IV, pp. 2, 1951.
    [14] O.L MacSorley, “High-Speed Arithmetic in Binary Computers”, IRE Proc., vol. 49, pp.67-91, Jan. 1961.
    [15] Smith, Michael J. S., “Application-Specific Integrated Circuits”, Addision-Wesley, Chapter 2.
    [16] Synopsys Design Compiler Reference Manual v1999.10”, Synopsys, 1999.
    [17] IC layout Command Reference Manual, Avanti 1999.4

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