Institute of Applied Microelectronics and Computer Engineering

College of Computer Science and Electrical Engineering, University of Rostock Slide 1

Spezielle Anwendungen des VLSI – Entwurfs

Applied VLSI design

Course and contest

Adder structures

Sebastian Kruse

Institute of Applied Microelectronics and Computer Engineering

College of Computer Science and Electrical Engineering, University of Rostock

Types of adders

Slide 2

• Redundant• Carry-Save (CSA)• Redundant-Binary (RBA)

• Not redundant (CPA)• Ripple-Carry (RCA), Manchester-Carry-Chain (MCC)• Carry-Skip (CSK), Carry-Select (CSEL)• Carry-Lookahead (CLA), Conditional-Sum (CSUM)• Asynchronous adder

Institute of Applied Microelectronics and Computer Engineering

College of Computer Science and Electrical Engineering, University of Rostock

Ripple-Carry adder

Slide 3

FA FA FA

s1 s0sn-1

cout cinc1c2cn-1

b0a0b1a1bn-1an-1

• Serialization of full adders• Small area but slow speed• In general the best adder for FPGA

• FPGA uses LUTs instead of AND, OR, XOR, NOT• Optimized logic which speeds up RCA

Delay time

Area

Institute of Applied Microelectronics and Computer Engineering

College of Computer Science and Electrical Engineering, University of Rostock

Carry-Skip adder

Slide 4

CPA CPA

   

CPA

   

     

     01

01

   

 

   

 

 

Delay time

Area

• Adder with square timing complexity and low area

• Area compared to RCA:

• Idea: parallel calculation

𝑠𝑖− 1:𝑘 𝑠𝑛− 1: 𝑖

Institute of Applied Microelectronics and Computer Engineering

College of Computer Science and Electrical Engineering, University of Rostock

Carry-Lookahead adder

Slide 5

 

 

CLA-Block  

    

Delay time

Area

• Fast adder with logarithm complexity but high area

• Idea: carry is calculated in advance

• Types of implementation (for carry generation)• Slansky• Kogge-Stone

…

• Brent-Kung• Han-Carlson

Institute of Applied Microelectronics and Computer Engineering

College of Computer Science and Electrical Engineering, University of Rostock

Brent-Kung

• Idea: use binary tree for carry propagation

• Two tree structures• Carry collection• Carry redistribution

Slide 6

Delay time

Area

carrytree

inversecarrytree

𝑐0𝑐1

𝑐2

𝑐3

𝑐4

𝑐5

𝑐6

𝑐7

(𝑔1 ,𝑝1)(𝑔0 ,𝑝0)

(𝑔3 ,𝑝3)(𝑔2 ,𝑝2)

(𝑔5 ,𝑝5)(𝑔4 ,𝑝4)

(𝑔7 ,𝑝7)(𝑔6 ,𝑝6)

Institute of Applied Microelectronics and Computer Engineering

College of Computer Science and Electrical Engineering, University of Rostock

Comparison on FPGA

Slide 7

• RCA• Area : 103• Max. frequency : 431,779 MHz

• CSK• Area : 125 • Max. frequency : 384,025 MHz

• Brent Kung• Area : 109• Max. frequency : 409,500 MHz

Institute of Applied Microelectronics and Computer Engineering

College of Computer Science and Electrical Engineering, University of Rostock

Comparison on ASIC

Slide 8

• RCA

• Core size : 4634,45 µm²

• Max. frequency : 3180 MHz

• Pdyn : 22,154 mW

• Pleak : 9,875 µW

• CSK

• Core size: 4324,63 µm²• Max. frequency : 2910MHz

• Pdyn : 18,651 mW

• Pleak : 8,346 µW

• Brent Kung• Core size : 4392,61 µm²• Max. frequency : 2980 MHz

• Pdyn : 19,406 mW

• Pleak : 8,716 µW

Institute of Applied Microelectronics and Computer Engineering

College of Computer Science and Electrical Engineering, University of Rostock

Thank you for your attention!

Slide 9

Institute of Applied Microelectronics and Computer Engineering

College of Computer Science and Electrical Engineering, University of Rostock

Half / full adder

Slide 10

FA

a b

cincout

s

HA

a b

cout

s

• Half adder ((2,2)-counter)

• Full adder ((3,2)-counter)

Institute of Applied Microelectronics and Computer Engineering

College of Computer Science and Electrical Engineering, University of Rostock

Comparison of adders

Slide 11

0 10 20Number of bits

0

20

40

60

80

0 10 20Number of bits

0

0.2

0.4

Brent-Kung

CSK

RCA Brent-Kung

RCA

t p(n

sec)

Are

a (m

m2)

Source: mountains.ece.umn.edu (2006)

CSK

Institute of Applied Microelectronics and Computer Engineering

College of Computer Science and Electrical Engineering, University of Rostock

Kogge-Stone

Slide 12