EE 5323 Project16 Bit Sklansky Adder

Phase 1 Report

Yuan Xu4139225

xuxxx488@umn.edu

Contents

• Literature review• Schematic• Netlist• Design Optimization• Waveforms of test cases• Power consumption at the maximum

operating frequency

Literature Review

• Sklansky adder belongs to tree adder family.• The difference between Sklansky adder and

other tree adders is prefix network.• Compare to other tree adders, Sklansky adder

has minimum logic levels, wiring tracks, but maxinum fanout. Also, it has largest delay at the same condition.

Literature review

1:0

2:03:0

3:25:47:69:811:1013:1215:14

6:47:410:811:814:1215:12

12:813:814:815:8

0123456789101112131415

15:014:013:012:011:010:0 9:0 8:0 7:0 6:0 5:0 4:0 3:0 2:0 1:0 0:0

Structure of 16 bit Sklansky Adder(Black square is dot operator

Grey square is empty dot operatorWhite triangle is buffer)

Reference List

• D.Harris, “ A Taxonomy of Parallel Prefix Networks, Signals ”, Systems and Computers, 2003. Conference Record of the Thirty-Seventh Asilomar Conference on, 2, 2213-2217 Vol.2,2003

• J. Sklansky, “Conditional-sum addition logic,” IRE Trans. Electronic Computers, vol. EC-9, pp. 226-231, June 1960.

• J M. Rabaey, A. Chandrakasan, B. Nikolic, “ Digital Integrated Circuits-A Design Perspective (Second Edition)”, Prentice Hall, 2003

Schematic of adder• Precomputation (Generating Propagate value

P and Generate value G). • Gi:i=Ai·Bi

• Pi:i=Ai B⊕ i

Schematic of adder

• Bubble shifted Dot operator

Schematic of adder• Empty empty dot operator

Schematic of adder• Bubble shifted empty dot operator

Schematic of adder• Overall view of adder

HSPICE netlist see attached file

• Sizing:• NMOS: L=50nm, W=90nm• PMOS: L=50nm, W=135nm• Temperature: 25°C

Design Optimization

• Sizing the gate to minimum size (90nm) can reduce area and power

• By using bubble shifting, we save totally 28 inverters, and 4 inverters on the critical path

• Adding the buffer can effectively reduce delay. Setting stage=1, fanout=4

Waveforms of test cases

• Worst case: For Sklansky adder, the worst case happens when inputs are 7FFF+0001. Since G will propagate from A_0 to S_15 which is the critical path.

Waveforms of test cases• Worst case 7FFF+0001• A_0-A_15 B_0-B_15 Cout,S_0-S_15,

Waveforms of test cases• Other cases( FFFF+0001, 7FFF+0001, 3FFF+0001, 1FFF+0001, 0FFF+0001, 07FF+0001,• 03FF+0001• A_0-A_15 B_0-B_15 Cout,S_0-S_15

Power consumption at the maxinum operating frequency, V=1.1V

• Worst case Delay= 4.11E-10 S• Ptotal=4.50E-05W

• Pmax=1.64E-03W