Design of a 32-Bit Hybrid Prefix-Carry Look-Ahead Adder

By  Sulabh Vidyarthi

HYBRID PREFIX-CLA

GOAL: To Implement a 32-bit hybrid prefix-carry-look-ahead adder.Implementation style to be used,static and dynamic.Test the design for Power and speed.

BACKGROUND

Parallel Prefix Adders(PPA):Carry operator “O” on (g,p) signal pairs

where,g=g”+p”g’p=p’p”

Operator “O” is associative =>[(g”’,P”’)

O(g”,p”)]O(g’,p’)=(g”’,p”’)O[(g”,p”)O(g’,p’)]

“O”

g’,p’

g”,p”

g,p

Parallel Prefix Adder(cont)

Given (p,g) terms for each bit ,they can be grouped together to find “all” the prefixes ,which is equivalent to computing all the carries in parallel.

Since operator “O” is commutative (g,p)’s can be grouped in any order.

However ,note that “O” is not commutative .

Conventional Prefix Adder(Brent-kung Adder)

Analysis Of PPA’s

Following highlight the characteristics of a general PPA:

Number of “O” cellsTree cell height(delay)Tree cell AreaCell fan-in and fan-outWiring congestion or wiring lengthDelay path variation(glitching)

Hybrid Prefix Carry Look-Ahead

Use of 4-bit Carry-look-ahead blocks to group g’s and p’s.Reduces the fan-in and fan-out of any operator “o” block to 2,which in turn reduces input capacitance and as a result faster carry propagation path.The wiring overhead is greatly reduced,which is very important at deep sub-micron levels as it reduces wiring capacitance and thus low power dissipation.Balanced Delay path (don’t want glitching).

HYBRID PREFIX-CLA(cont)

Analysis of DesignL1: g,p generation using inputs A and BL2:Grouping of g and p to generate group carry G and P( G0 G4---G28,P0 P4---P28)L3:Using Operator “O” on the group G and P to generate Gr4 and Pr4eg:Gr4=G4+P4.G0,Pr4=P0P4L4: Carry generator.eg C4=Gr4+Pr4.C0L5:Sum generation using 4-bit carry look-ahead generator

Analysis(cont)

Delay Analysis:

L1(1T) + L2(3T) + L3(2T) + L4(2T)+L5(2T)=10T

The critical path is through L1-L4 + One CLA Adder unit in L5.

T=one gate delay

Tool Flow

Gate level design of the static and dynamic adders :verilog(Modelsim)Extraction to transistor level (Synopsys and Cadence)Delay and power analysis :Cadence

Result

Worst case delay and power estimate

Avg delay

Power PDP

Static 1.5ns 2.3mW 2.53E-12

Dynamic

1.1ns 6.5mW 7.15E-12

ConclusionStatic and dynamic design both are faster than the normal look-ahead adders.Easy implementation and simple design using only AND,OR and XOR gates .Static design has obvious power advantages over the dynamic design.The high power dissipation of dynamic design outweighs its advantages of high speed.The Hybrid Prefix CLA has definite speed advantage over several other adders.Reduction in power dissipation in Domino and Dual rail Domino is a potential research area.Techniques such as using Mixed-Swing Dual Rail Domino topology* can give Hybrid Prefix adders and edge over other adder types both in terms of speed and Power.

*Mixed-Swing Quad- Rail for Low Power Dual-Rail Domino Logic(Bharath Ramasubramanian,L. Richard,Herman Schmit)

References[1] R. P. Brent and H. T. Kung, “A regular layout for parallel adders,” IEEE Transactions on Computers, vol. C-31, no. 3, March 1982, pp. 260-4.

[2] P. M. Kogge and H. S. Stone, “A Parallel Algorithm for the Efficient Solution of a General Class of Recurrence Equations,” IEEE Transactions on Computers, vol. C-22, no. 8, August 1973, pp. 786-93. [3] H. Ling, “High-Speed Binary Adder,” IBM Journal of Research and Development, vol. 25, no. 2-3, May-June 1981, pp. 156-66. [4] V. G. Oklobdzija and E. R. Barnes, “On implementing addition in VLSI technology,” Journal of Parallel and Distributed Computing, vol. 5, no. 6, December 1988, pp.716-28. [5] T. Han, D. A. Carlson, and S. P. Levitan, “VLSI Design of High-Speed Low-Area Addition Circuitry,” Proceedings of the IEEE International Conference on Computer Design: VLSI in Computers and Processors, 1987, pp. 418-22. [6] J. M. Rabaey, Digital Integrated Circuits: A Design Perspective, Prentice Hall, New Jersey, 2002. [7] Behrooz Parhami, Computer Arithmetic Algorithms and Hardware design Oxford university Press, 2000.