DOC PREVIEW
Berkeley ELENG 141 - Lecture 28 Adders, Multipliers ROM

This preview shows page 1-2 out of 7 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 7 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 7 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 7 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

EE1411EE1411EECS141EE141EE141--Fall 2006Fall 2006Digital Integrated Digital Integrated CircuitsCircuitsLecture 28Lecture 28Adders, MultipliersAdders, MultipliersROMROMEE1412EECS141AnnouncementsAnnouncements Homework 10 due on ThursdayEE1413EECS141Class MaterialClass Material Last lecture Adders Today’s lecture Finish adders Multipliers ROM Reading Chapters 11, 12EE1414EECS141CarryCarry--LookaheadLookaheadAddersAddersEE1415EECS141LookaheadLookahead--Basic IdeaBasic IdeaCok,fAkBkCok,1–,,()GkPkCok 1–,+==AN-1, BN-1A1, B1P1S1••••••SN-1PN-1Ci, N-1S0P0Ci,0Ci,1A0, B0EE1416EECS141LookaheadLookahead: Topology: TopologyCok,GkPkGk1–Pk1–Cok 2–,+()+=Cok,GkPkGk1–Pk1–…P1G0P0Ci0,+()+()+()+=Expanding Lookahead equations:All the way:Co,3Ci,0VDDP0P1P2P3G0G1G2G3EE1412EE1417EECS141Logarithmic LookLogarithmic Look--Ahead AdderAhead AdderA7FA6A5A4A3A2A1A0A0A1A2A3A4A5A6A7Ftp∼ log2(N)tp∼ NEE1418EECS141Carry Carry LookaheadLookaheadTreesTreesCo0,G0P0Ci0,+=Co1,G1P1G0P1P0Ci0,++=Co2,G2P2G1P2P1G0P+2P1P0Ci0,++=G2P2G1+()=P2P1()G0P0Ci0,+()+G2:1P2:1Co0,+=Can continue building the tree hierarchically.EE1419EECS141Tree AddersTree Adders16-bit radix-2 Kogge-Stone tree(A0, B0)(A1, B1)(A2, B2)(A3, B3)(A4, B4)(A5, B5)(A6, B6)(A7, B7)(A8, B8)(A9, B9)(A10, B10)(A11, B11)(A12, B12)(A13, B13)(A14, B14)(A15, B15)S0S1S2S3S4S5S6S7S8S9S10S11S12S13S14S15EE14110EECS141Tree AddersTree Adders(a0, b0)(a1, b1)(a2, b2)(a3, b3)(a4, b4)(a5, b5)(a6, b6)(a7, b7)(a8, b8)(a9, b9)(a10, b10)(a11, b11)(a12, b12)(a13, b13)(a14, b14)(a15, b15)S0S1S2S3S4S5S6S7S8S9S10S11S12S13S14S1516-bit radix-4 Kogge-Stone TreeEE14111EECS141Sparse TreesSparse Trees(a0, b0)(a1, b1)(a2, b2)(a3, b3)(a4, b4)(a5, b5)(a6, b6)(a7, b7)(a8, b8)(a9, b9)(a10, b10)(a11, b11)(a12, b12)(a13, b13)(a14, b14)(a15, b15)S1S3S5S7S9S11S13S15S0S2S4S6S8S10S12S1416-bit radix-2 sparse tree with sparseness of 2EE14112EECS141Tree AddersTree Adders(A0, B0)(A1, B1)(A2, B2)(A3, B3)(A4, B4)(A5, B5)(A6, B6)(A7, B7)(A8, B8)(A9, B9)(A10, B10)(A11, B11)(A12, B12)(A13, B13)(A14, B14)(A15, B15)S0S1S2S3S4S5S6S7S8S9S10S11S12S13S14S15Brent-Kung TreeEE1413EE14113EECS141Example: Domino AdderExample: Domino AdderVDDClkPi= ai + biClkaibiVDDClkGi = aibiClkaibiPropagate GenerateEE14114EECS141Example: Domino AdderExample: Domino AdderVDDClkkPi:i-k+1Pi-k:i-2k+1Pi:i-2k+1VDDClkkGi:i-k+1Pi:i-k+1Gi-k:i-2k+1Gi:i-2k+1Propagate GenerateEE14115EECS141Example: Domino SumExample: Domino SumVDDClkGi:0ClkSumVDDClkdClkGi:0ClkSi1ClkdSi0KeeperEE14116EECS141ZX··Y× Zk2kk0=MN1–+∑==Xi2ii0=M1–∑⎝⎠⎜⎟⎜⎟⎜⎟⎛⎞Yj2jj0=N1–∑⎝⎠⎜⎟⎜⎟⎜⎟⎛⎞=XiYj2ij+j0=N1–∑⎝⎠⎜⎟⎜⎟⎜⎟⎛⎞i0=M1–∑=XXi2ii0=M1–∑=YYj2jj0=N1–∑=withThe Binary MultiplicationThe Binary MultiplicationEE14117EECS141x+Partial productsMultiplicandMultiplierResult1 0 1 0 1 01 0 1 0 1 01 0 1 0 1 01 1 1 0 0 1 1 1 00 0 0 0 0 01 0 1 0 1 01 0 1 1The Binary MultiplicationThe Binary MultiplicationEE14118EECS141Y0Y1X3X2X1X0X3HAX2FAX1FAX0HAY2X3FAX2FAX1FAX0HAZ1Z3Z6Z7Z5Z4Y3X3FAX2FAX1FAX0HAZ2Z0The Array MultiplierThe Array MultiplierEE1414EE14119EECS141HA FA FA HAHAFAFAFAFAFA FA HACritical Path 1Critical Path 2Critical Path 1 & 2()()[]()()andsumcarrymulttNtNtNMt⋅−+⋅−+⋅−+−≈ 1121The MThe M--byby--N Array Multiplier: N Array Multiplier: Critical PathCritical PathEE14120EECS141ABPCiVDDAAAVDDCiAPABVDDVDDCiCiCoSCiPPPPPSum GenerationCarry GenerationSetupTransmissionTransmission--Gate Full AdderGate Full AdderBalanced tsumand tcarryEE14121EECS141CarryCarry--Save MultiplierSave MultiplierHA HA HA HAFAFAFAHAFAHA FA FAFAHA FA HAVector Merging Adder() ()mergeandcarrymultttNtNt +⋅−+⋅−= 11EE14122EECS141Multiplier Multiplier FloorplanFloorplanSCSCSCSCSCSCSCSCSCSCSCSCSCSCSCSCZ0Z1Z2Z3Z4Z5Z6Z7X0X1X2X3Y1Y2Y3Y0Vector Merging CellHA Multiplier CellFA Multiplier CellX and Y signals are broadcastedthrough the complete array.( )EE14123EECS141WallaceWallace--Tree MultiplierTree Multiplier6543210 6543210Partial products First stageBit position6543210 6543210Second stage Final adderFA HA(a) (b)(c) (d)EE14124EECS141WallaceWallace--Tree MultiplierTree MultiplierPartial productsFirst stageSecond stageFinal adderFA FA FAHA HAFAx3y3z7z6z5z4z3z2z1z0x3y2x2y3x1y1x3y0x2y0x0y1x0y2x2y2x1y3x1y2x3y1x0y3x1y0x0y0x2y1EE1415EE14125EECS141WallaceWallace--Tree MultiplierTree MultiplierFAFAFAFAy0y1y2y3y4y5SCi-1Ci-1Ci-1CiCiCiFAy0y1y2FAy3y4y5FAFACCSCi-1Ci-1Ci-1CiCiCiEE14126EECS141Multipliers Multipliers ––SummarySummary Optimization goals different than in binary adder Once again: Identify critical path Other possible techniques Logarithmic versus linear (Wallace Tree Mult) Data encoding (Booth) PipeliningFirst glimpse at system level optimizationEE14127EECS141Other Types of Other Types of MemoryMemoryEE14128EECS141Semiconductor Memory ClassificationSemiconductor Memory ClassificationRead-Write MemoryNon-VolatileRead-WriteMemoryRead-Only MemoryEPROME2PROMFLASHRandomAccessNon-RandomAccessSRAM DRAMMask-ProgrammedProgrammable (PROM)FIFOShift RegisterCAMLIFOEE14129EECS141ReadRead--Only Memory CellsOnly Memory CellsWLBLWLBL1WLBLWLBLWLBL0VDDWLBLGNDDiode ROM MOS ROM 1 MOS ROM 2EE14130EECS141MOS OR ROMMOS OR ROMWL[0]VDDBL[0]WL[1]WL[2]WL[3]VbiasBL[1]Pull-down loadsBL[2] BL[3]VDDEE1416EE14131EECS141MOS NOR ROMMOS NOR ROMWL[0]GNDBL[0]WL[1]WL[2]WL[3]VDDBL[1]Pull-up devicesBL[2] BL [3]GNDEE14132EECS141MOS NOR ROM LayoutMOS NOR ROM LayoutProgrammming using theActive Layer OnlyPolysiliconMetal1DiffusionMetal1 on DiffusionCell (9.5λ x 7λ)EE14133EECS141MOS NOR ROM LayoutMOS NOR ROM LayoutPolysiliconMetal1DiffusionMetal1 on DiffusionCell (11λ x 7λ)Programmming usingthe Contact Layer OnlyEE14134EECS141MOS NAND ROMMOS NAND ROMAll word lines high by default with exception of selected rowWL[0]WL[1]WL[2]WL[3]VDDPull-up devicesBL[3]BL[2]BL[1]BL[0]EE14135EECS141MOS NAND ROM LayoutMOS NAND ROM LayoutNo contact to VDD or GND necessary;Loss in performance compared to NOR ROMdrastically reduced cell sizePolysiliconDiffusionMetal1 on DiffusionCell (8λ x 7λ)Programmming usingthe Metal-1 Layer OnlyEE14136EECS141NAND ROM LayoutNAND ROM LayoutCell (5λ x 6λ)PolysiliconThreshold-alteringimplantMetal1 on DiffusionProgrammming usingImplants OnlyEE1417EE14137EECS141Equivalent Transient Model for MOS NOR ROMEquivalent Transient Model for MOS NOR ROM Word line parasitics Wire capacitance and gate capacitance


View Full Document

Berkeley ELENG 141 - Lecture 28 Adders, Multipliers ROM

Documents in this Course
Adders

Adders

7 pages

Memory

Memory

33 pages

I/O

I/O

14 pages

Lecture 8

Lecture 8

34 pages

Lab 3

Lab 3

2 pages

I/O

I/O

17 pages

Project

Project

6 pages

Adders

Adders

15 pages

SRAM

SRAM

13 pages

Load more
Download Lecture 28 Adders, Multipliers ROM
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Lecture 28 Adders, Multipliers ROM and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Lecture 28 Adders, Multipliers ROM 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?