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111adder

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Peeyush Pashine
Peeyush Pashine
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Adder comparisons and New (1,1,1)adder Peeyush Pashine 2011H140033H
Brent Kung adder
Sklansky adder (p8, g8) (p7, g7) (p6, g6) (p5, g5) (p4, g4) (p3, g3) (p2, g2) (p1, g1) c8 c7 c6 c5 c4 c3 c2 c1
Skalnsky adder 16 bit 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 15:1 13:1 11:1 9: 7: 5: 3: 1: 4 2 0 8 6 4 2 0 15:1 14:1 11: 10: 7: 6: 3: 2: 2 2 8 8 4 4 0 0 15: 14: 13: 12: 8 8 8 8 15:014:013:0 12:011:010:0 9:0 8:0 7:0 6:0 5:0 4:0 3:0 2:0 1:0 0:0
Ladner fischer adder 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 15:14 13:12 11:10 9:8 7:6 5:4 3:2 1:0 15:12 11:8 7:4 3:0 15:8 13:8 7:0 5:0 15:8 13:0 11:0 9:0 15:0 14:0 13:0 12:0 11:0 10:0 9:0 8:0 7:0 6:0 5:0 4:0 3:0 2:0 1:0 0:0
Kogge stone adder 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 15:14 14:13 13:12 12:11 11:10 10:9 9:8 8:7 7:6 6:5 5:4 4:3 3:2 2:1 1:0 15:12 14:11 13:10 12:9 11:8 10:7 9:6 8:5 7:4 6:3 5:2 4:1 3:0 2:0 15:8 14:7 13:6 12:5 11:4 10:3 9:2 8:1 7:0 6:0 5:0 4:0 15:0 14:0 13:0 12:0 11:0 10:0 9:0 8:0 7:0 6:0 5:0 4:0 3:0 2:0 1:0 0:0
Classical prefix adders 8 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1 8:1 7:1 6:1 5:1 4:1 3:1 2:1 1 8:1 7:1 6:1 5:1 4:1 3:1 2:1 1 8:1 7:1 6:1 5:1 4:1 3:1 2:1 1 Brent-Kung: Sklansky: Kogge-Stone: Logical levels: 2log2n–1 Logical levels: log2n Logical levels: log2n Max fanouts: 2 Max fanouts: n/2 Max fanouts: 2 Wire tracks: 1 Wire tracks: 1 Wire tracks: n/2 7
Knowles 2,1,1,1
Knowles 4,2,1,1
Topology of some prefix adders Brent-Kung topology (Minimum fan-out) Knowles topologies (Varied fan-out at each level ) Ladner-Fischer topology (Minimum depth, high fanout)
Prefix adder taxonomy
New (1,1,1) Adder
12 11 10 9 8 7 6 5 4 3 2 1 12:1 11:1 10:1 9:1 8:1 7:1 6:1 5:1 4:1 3:1 2:1 1

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111adder

  • 1. Adder comparisons and New (1,1,1)adder Peeyush Pashine 2011H140033H
  • 3. Sklansky adder (p8, g8) (p7, g7) (p6, g6) (p5, g5) (p4, g4) (p3, g3) (p2, g2) (p1, g1) c8 c7 c6 c5 c4 c3 c2 c1
  • 4. Skalnsky adder 16 bit 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 15:1 13:1 11:1 9: 7: 5: 3: 1: 4 2 0 8 6 4 2 0 15:1 14:1 11: 10: 7: 6: 3: 2: 2 2 8 8 4 4 0 0 15: 14: 13: 12: 8 8 8 8 15:014:013:0 12:011:010:0 9:0 8:0 7:0 6:0 5:0 4:0 3:0 2:0 1:0 0:0
  • 5. Ladner fischer adder 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 15:14 13:12 11:10 9:8 7:6 5:4 3:2 1:0 15:12 11:8 7:4 3:0 15:8 13:8 7:0 5:0 15:8 13:0 11:0 9:0 15:0 14:0 13:0 12:0 11:0 10:0 9:0 8:0 7:0 6:0 5:0 4:0 3:0 2:0 1:0 0:0
  • 6. Kogge stone adder 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 15:14 14:13 13:12 12:11 11:10 10:9 9:8 8:7 7:6 6:5 5:4 4:3 3:2 2:1 1:0 15:12 14:11 13:10 12:9 11:8 10:7 9:6 8:5 7:4 6:3 5:2 4:1 3:0 2:0 15:8 14:7 13:6 12:5 11:4 10:3 9:2 8:1 7:0 6:0 5:0 4:0 15:0 14:0 13:0 12:0 11:0 10:0 9:0 8:0 7:0 6:0 5:0 4:0 3:0 2:0 1:0 0:0
  • 7. Classical prefix adders 8 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1 8:1 7:1 6:1 5:1 4:1 3:1 2:1 1 8:1 7:1 6:1 5:1 4:1 3:1 2:1 1 8:1 7:1 6:1 5:1 4:1 3:1 2:1 1 Brent-Kung: Sklansky: Kogge-Stone: Logical levels: 2log2n–1 Logical levels: log2n Logical levels: log2n Max fanouts: 2 Max fanouts: n/2 Max fanouts: 2 Wire tracks: 1 Wire tracks: 1 Wire tracks: n/2 7
  • 10. Topology of some prefix adders Brent-Kung topology (Minimum fan-out) Knowles topologies (Varied fan-out at each level ) Ladner-Fischer topology (Minimum depth, high fanout)
  • 13. 12 11 10 9 8 7 6 5 4 3 2 1 12:1 11:1 10:1 9:1 8:1 7:1 6:1 5:1 4:1 3:1 2:1 1