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L5 Adders

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Adder Circuits
Acknowledgement ,[object Object],[object Object]
Outline ,[object Object],[object Object]
A Generic Digital Processor
Building Blocks for Digital Architectures Arithmetic unit - Bit-sliced datapath (adder, multiplier, shifter, comparator, etc.) Memory - RAM, ROM, Buffers, Shift registers Control - Finite state machine (PLA, random logic.) - Counters Interconnect - Switches - Arbiters - Bus
Bit-Sliced Design
Bit-Sliced Datapath
Itanium Integer Datapath Fetzer, Orton, ISSCC’02
Full-Adder
The Binary Adder
Express Sum and Carry as a function of P, G, D Define 3 new variable which ONLY depend on A, B Generate (G) = AB Propagate (P) = A  B Delete = A B Can also derive expressions for S and C o based on D and P Propagate (P) = A  B Note that we will be sometimes using an alternate definition for
The Ripple-Carry Adder Worst case delay linear with the number of bits Goal: Make the fastest possible carry path circuit t d = O( N ) t adder = ( N-1 ) t carry + t sum
Complimentary Static CMOS Full Adder 28 Transistors
Inversion Property
Minimize Critical Path by Reducing Inverting Stages Exploit Inversion Property
A Better Structure: The Mirror Adder
Mirror Adder Stick Diagram
The Mirror Adder ,[object Object],[object Object],[object Object],[object Object],[object Object]
Transmission Gate Full Adder
Manchester Carry Chain
Manchester Carry Chain
Manchester Carry Chain Stick Diagram
Carry-Bypass Adder Also called Carry-Skip
Carry-Bypass Adder (cont.) t adder = t setup + Mt carry + ( N/M -1) t bypass + ( M -1) t carry + t sum
Carry Ripple versus Carry Bypass
Carry-Select Adder
Carry Select Adder: Critical Path
Linear Carry Select
Square Root Carry Select
Adder Delays - Comparison
LookAhead - Basic Idea
Look-Ahead: Topology Expanding Lookahead equations: All the way:
Logarithmic Look-Ahead Adder
Carry Lookahead Trees Can continue building the tree hierarchically.
Tree Adders 16-bit radix-2 Kogge-Stone tree
Tree Adders 16-bit radix-4 Kogge-Stone Tree
Sparse Trees 16-bit radix-2 sparse tree with sparseness of 2
Tree Adders Brent-Kung Tree
Example: Domino Adder Propagate Generate
Example: Domino Adder Propagate Generate
Example: Domino Sum

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L5 Adders