1. Array Multiplier Haibin Wang Qiong Wu

2. Outlines Background & Motivation Principles Implementation & Simulation Advantages & Disadvantages Conclusions

3. Background & Motivation One of the most critical functions carried out by ALU Digital multiplication is the most extensively used operation (especially in signal processing), people who design digital signal processors sacrifice a lot of chip area in order to make the multiply as fast as possible Innumerable schemes have been proposed for realization of the operation

4. Multiplication Schemes Serial Multiplication (Shift-Add) Computing a set of partial products, and then summing the partial products together. The implementations are primitive with simple architectures (used when there is a lack of a dedicated hardware multiplier) Parallel Multiplication Partial products are generated simultaneously Parallel implementations are used for high performance machines, where computation latency needs to be minimized

5. Principles of Array Multiplier 4*4 bit multiplication a3a3 a2a2 a1a1 a0a0 × b3b3 b2b2 b1b1 b0b0 a3b0a3b0 a2b0a2b0 a1b0a1b0 a0b0a0b0 a3b1a3b1 a2b1a2b1 a1b1a1b1 a 0 b1 a3b2a3b2 a2b2a2b2 a1b2a1b2 a0b2a0b2 a3b3a3b3 a3b2a3b2 a3b1a3b1 a3b0a3b0 p7p7 p6p6 p5p5 p4p4 p3p3 p2p2 p1p1 p0p0

6. For 4*4 Array Multiplier, it needs 16 AND gates, 4 HAs, 8FAs (total 12 Adders) For m*n Array Multiplier, it needs m*n AND gates, n HAs, (m-2)*n FAs, (total (m-1)*n Adders)

7. Principles of Array Multiplier(Cont.)

9. Implementation & Simulation Verilog (ISE 10.1) Multiplier Design Cell: MulCell Multiplier: ArrayMult Testbench Stimulus Verification & Timing

10. Cell

11. Multiplier

12. Simulation Result & Timing

13. Advantages & Disadvantages Advantages : Minimum complexity Easily scalable Easily pipelined Regular shape, easy to place & route Disadvantages : High power consumption More digital gates resulting in large chip area

14. Conclusions Array multiplier is implemented and verified in Verilog Although it utilizes more gates, the performance can easily be increased using pipeline technique As a parallel multiplication method, array multiplier outperforms serial multiplication schemes in terms of speed.

15. Reference [1]. http://www.trivology.com/articles/534/what-is-an- array-multiplier.htmlhttp://www.trivology.com/articles/534/what-is-an- array-multiplier.html [2]. http://ece.gmu.edu ece645_lecture7.ppthttp://ece.gmu.edu

16. Questions?