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chapter5-datapath02

# chapter5-datapath02 - Manchester Carry Chain Digital IC 1...

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Digital IC Manchester Carry Chain 1

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Digital IC 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 Slide 2 in + S 4:1 P 4:1 A 4:1 + S 8:5 P 8:5 A + S 12:9 P 12:9 A 12:9 B 12:9 + S 16:13 B 16:13 C out C 4 1 0 C 0 C 12 1 0 1 0
Digital IC 4/16 bit Block Carry Skip Adder Worst-case delay carry from bit 0 to bit 15 = carry generated in bit 0, ripples through bits 1, 2, and 3, skips the middle two groups (B is the group size in bits), ripples in the last group from bit 12 to bit 15 C i,0 Sum Carry Propagation Setup Sum Carry Propagation Setup Sum Carry Propagation Setup Sum Carry Propagation Setup bits 0 to 3 bits 4 to 7 bits 8 to 11 bits 12 to 15 T add = t setup + B t carry + ((N/B) - 1) t skip +(B-1) t carry + t sum

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Digital IC RCA, Carry Skip Adder Comparison 0 10 20 30 40 50 60 70 8 bits 16 bits 32 bits 48 bits 64 bits RCA CSkA B=2 B=3 B=4 B=5 B=6
Digital IC Carry-Skip PG Diagram Slide 6 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 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 16:0 skip t : : : 1: : : i j i k i k k j i j i k k j G G P G P P P  0 : 0 1 : 4 1 : 4 0 : 4 G P G G 0 : 4 5 : 8 5 : 8 0 : 8 G P G G 0 : 8 9 : 12 9 : 0 : G P G G 0 : 13 : 16 : 0 : G P G G

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Digital IC Carry-Skip PG Diagram Slide 7   skip xor 2 1 ( 1) pg AO t t n k t t   0 : 0 1 : 4 1 : 4 0 : 4 G P G G 0 : 4 5 : 8 5 : 8 0 : 8 G P G G 0 : 8 9 : 12 0 : 0 : G P G G 0 : 13 : 16 : 0 : G P G G 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 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 16:0
Digital IC Carry-Skip PG Diagram 8 0 , 0 1 , 4 1 , 4 0 , 4 G P G G P.CHAN and M.Schlag,”Analysis and design of CMOS Manchester adders with variable carry- skip” IEEE Trans.Computers ,Vol.39,No.8,Aug.1990,pp.983-992

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Digital IC Variable Group Size 0 3 4 5 6 7 8 9 10 11 12 13 14 15 16 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 16:0 Slide 9 Delay grows as O(sqrt(N))
Digital IC 10 C ok fA k B k C 1   G k P k C o k 1 + == A N- 1 , B N- 1 A 1 , B 1 P 1 S 1 ??? S N- 1 P N- 1 C i , N- 1 S 0 P 0 C i ,0 C i ,1 A 0 , B 0

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Digital IC Look-Ahead: Topology 11 C ok G k P k G k1 P C o k 2 +  + = C G k P k G P P 1 G 0 P 0 C i0 + + + + = Expanding Lookahead equations: All the way: C o ,3 C i ,0 V DD P 0 P 1 P 2 P 3 G 0 G 1 G 2 G 3

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chapter5-datapath02 - Manchester Carry Chain Digital IC 1...

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