Design and Implementation of VLSI Systems

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Design and Implementation of VLSI
Systems (EN1600) Lecture 27 Datapath Subsystems
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Prof. Sherief Reda Division of Engineering, Brown
University Spring 2008
sources Weste/Addison Wesley Rabaey/Pearson
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Manchester carry adder

• Using transmission gates
• Using dynamic gates

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Manchester carry chains
Critical path involves a series propagate
transistor for each bit ? a significant over
carry-ripple (which used majority or AND-OR gate)
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Equivalence circuits for Manchester carry chain
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Carry skip adder
A0
B0
A1
B1
A2
B2
A3
B3
Co,3
Ci,0
FA
FA
FA
FA
Co,3
S0
S1
S2
S3
BP P0 P1 P2 P3 Block Propagate
If (P0 P1 P2 P3 1) then Co,3 Ci,0
otherwise the block itself kills or generates the
carry internally
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Carry-skip adder

• Carry-ripple is slow through all N stages
• Carry-skip allows carry to skip over groups of n
  bits
• Decision based on n-bit propagate signal

Original design by Charles Babbage
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Carry-lookahead adder
Similar to the carry-skip adder, but computes
generate signals as well as group propagate
signals to avoid waiting for a ripple to
determine if the group generates a carry.
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Carry-select adder

• One adder calculates the sums assuming a carry-n
  of 0 while the other calculates the sums assuming
  a carry-in of 1.
• The actual carry triggers a multiplexer that
  chooses the appropriate sum

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II. Comparators

• 0s detector and 1s detectors
• Equality comparator A B
• Magnitude comparator A lt B

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A. 1s and 0s detectors

• 1s detector N-input AND gate
• 0s detector NOTs 1s detector (N-input NOR)

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B. Equality comparator

• Check if each bit is equal (XNOR, aka equality
  gate)
• 1s detect on bitwise equality

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C. Magnitude comparator

• Compute B-A and look at sign
• B-A B A 1
• For unsigned numbers, carry out is sign bit