Integer Multipliers

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1、IntegerMultipliers1AXPBMultipliers•AmusthavecircuitinmostDSPapplications•Avarietyofmultipliersexiststhatcanbechosenbasedontheirperformance•Serial,Serial/Parallel,ShiftandAdd,Array,Booth,WallaceTree,….2AXPBreseentreesnetconverterRA16x16reConvertersenmult

2、iplierRCetconverterRB3AXPBMultiplicationAlgorithmX=Xn-1Xn-2…………………X0MultiplicandY=Yn-1Yn-2…………………….Y0MultiplierYn-1X0Yn-2X0Yn-3X0……Y1X0Y0X0Yn-1X1Yn-2X1Yn-3X1……Y1X1Y0X1Yn-1X2Yn-2X2Yn-3X2……Y1X2Y0X2…………….….….….….Yn-1Xn-2Yn-2X0n-2Yn-3Xn-2……Y1Xn-2Y0Xn-2Yn-1X

3、n-1Yn-2X0n-1Yn-3Xn-1……Y1Xn-1Y0Xn-1-----------------------------------------------------------------------------------------------------------------------------------------P2n-1P2n-2P2n-3P2P1P041.MultiplicationAlgorithmsImplementationofmultiplicationofbi

4、narynumbersboilsdowntohowtodothetheadditions.Considerthetwo8bitnumbersAandBtogeneratethe16bitproductP.Firstgeneratethe64partialProductsandthenaddthemup.A7A6A5A4A3A2A1A0B7B6B5B4B3B2B1B0A7.B0A6.B0A5.B0A4.B0A3.B0A2.B0A1.B0A0.B0A7.B1A6.B1A5.B1A4.B1A3.B1A2.B

5、1A1.B1A0.B1A7.B2A6.B2A5.B2A4.B2A3.B2A2.B2A1.B2A0.B2A7.B3A6.B3A5.B3A4.B3A3.B3A2.B3A1.B3A0.B3A7.B4A6.B4A5.B4A4.B4A3.B4A2.B4A1.B4A0.B4A7.B5A6.B5A5.B5A4.B5A3.B5A2.B5A1.B5A0.B5.A7.B6A6.B6A5.B6A4.B6A3.B6A2.B6A1.B6A0.B6A3.B7A2.B7A1.B7A0.B7A3.B7A2.B7A1.B7A0.B7P

6、15P14P13P12P11P10P9P8P7P6P5P4P3P2P1P0Theequationis:.m1n1ijP(mn)A(m)B(n)ab2iji0j05AXPMultiplierDesignBStorageRERGEIMUGN(16X16Multiplier1Unit)OUTControlUnit6X:x3x2x1x0Y:y3y2y1y0InputSequenceforG1:A00x3x2x1x00x3x2x1x00x3x2x1x00x3x2x1x0XPB00y3y3y3y30y2y2y2y

7、20y1y1y1y10y0y0y0y0Reset:010000100001000010000dq01-bitReset=0G2REGCLK100xy00+0000x00G1xyy000SerialRegisterCLKCLK/(N+1)Slide17S:theithbitofthefinalresultX:x3x2x1x0Y:y3y2y1y0iInputSequenceforG1:00x3x2x1x00x3x2x1x00x3x2x1x00x3x2x1x000y3y3y3y30y2y2y2y20y1y1

8、y1y10y0y0y0y0Reset:010000100001000010000dq01-bitReset=0G2REGCLK100xy10S000+0x10G1xyy100SerialRegisterCLKCLK/(N+1)Slide28S:theithbitofthefinalresultX:x3x2x1x0Y:y3y2y1y0iInputSequenceforG1:00x3x2x1x00x3x2x1x00x3x2x1x00x3x2x1x000y3y