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Carry-Select Adders. Consider the Following Partitioned Addition:. 101 +110. 101 +111. 110 +001. 1  011  0. 100  0. 111  0. 1  100  1. 101  1. 000  1. 1 100 100 111. 4-Bit Carry Select. X = 1 0 1 1 0 1 1 0 +Y = 0 0 1 0 1 1 0 1

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carry select adders
Carry-Select Adders
  • Consider the Following Partitioned Addition:

101

+110

101

+111

110

+001

1  011  0

100  0

111  0

1  100  1

101  1

000  1

1 100 100 111

4 bit carry select
4-Bit Carry Select

X = 1 0 1 1 0 1 1 0

+Y = 0 0 1 0 1 1 0 1

sum 1 1 0 1 0 0 1 1

cout 0 1

sum 1 1 1 0

cout 0

}

cin = 0

}

cin = 1

  • Answer: 1110 0011
  • cin 1 for Least Significant Nibble
  • Must Wait for 4 “Ripples” to Select
  • Can Divide into Groups of Two
2 bit carry select
2-Bit Carry Select

X = 1 0 1 1 0 1 1 0

+Y = 0 0 1 0 1 1 0 1

sum 1 0 0 1 0 0 1 1

cout 0 1 1 0

sum 1 1 1 0 0 1

cout 0 1 1

}

cin = 0

}

cin = 1

  • Answer: 11 10 00 11
  • cin 1 for Least Significant 2 Bits
  • Must Wait for 2 “Ripples” to Select
  • Can Divide into Groups of One – Carry Select
1 bit carry select cond sum
1-Bit Carry-Select/Cond. Sum

X = 1 0 1 1 0 1 1 0

+Y = 0 0 1 0 1 1 0 1

sum 1 0 0 1 1 0 1 1

cout 0 0 1 0 0 1 0 0

sum 0 1 1 0 0 1 0

cout 1 0 1 1 1 1 1

}

cin = 0

}

cin = 1

  • Answer: 11 10 00 11
  • cin 1 for Least Significant 1 Bit
  • Must Wait for 1 “Ripples” to Select
  • Can Divide into Groups of One – Conditional Sum
optimizations implementation
Optimizations/Implementation
  • Carry Select/Conditional Sum Implemented as Adders with MUX Tree (1-bit Cells for Conditional Sum)
  • Carry Select is Conditional Sum with One Set of Groups - Not Necessarily with Group Size = 1
  • CLA/Conditional Sum Approximately Same Speed
  • CLA Generally has More Efficient Layout
  • Trees are Hard (irregular) – CLA More Popular
  • Prefix Generators are Optimal in speed/area Tradeoff