/966 Bit level dependence Graph a3 a0 a3 a2 al b0 X/ b b3 X+ 3 X3 Sin ain 3 x0 Broadcast si goals: bin bout bout=bin:aout=ain x/ Cout Cin Single-bit Full-Adder: 2 Cout++Sout ain*bin Sin Cin Dash line means carry-ripple 30t Sout 个 Carry out 2021年2月 11
Bit level dependence Graph 2021年2月 11 Dash line means carry-ripple Carry out
/966 The carry-propagation limits the speed of multiplication. a.3 a0 1十 b 3 xO Critical path after pipeline 2021年2月 12
The carry-propagation limits the speed of multiplication. 2021年2月 12 Critical path after pipeline
13.2.1.2 Parallel Carry-save array multipliers 96 In a case involving several additions,such as partial product accumulation in multiplication,it is not strictly necessary to propagate these carries during each cycle. Instead,the carries generated during the addition of a pair of operands can be saved and added,with proper alignment,to the next operands. 01100 01100 0.75*0.75 01100 01 100 000000 000000 00000 00000 000000 000000 01100 01100 0001100 0011 00 001100 01100 110010 001010 00000 00000 1 0 0 01001 01001 2021年2月 13
13.2.1.2 Parallel Carry-save array multipliers In a case involving several additions, such as partial product accumulation in multiplication, it is not strictly necessary to propagate these carries during each cycle. Instead, the carries generated during the addition of a pair of operands can be saved and added, with proper alignment, to the next operands. 2021年2月 13 0.75*0.75 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1
U 966 a3 a2 0 0 a3 a2 b b2 b3 b3 b3 Vector Merging Addcr Vector Merging Adder xl xO 3 x2 Sio Cin ain Bcoadca文signals: bio bout bout-bin:aout-ain x/+ Slogle-blt Full-Adder: tt 2 Cout Sour =aio"bin Sin Cin Cout aout Sour 2021年2月 14
2021年2月 14
/966 Vector merging Adder HA (b) x2 悦单 (a) (c) Fig.13.7 Vector merging for 4 x 4-bit parallel carry-save multiplication:(a)carry- save vector merging,(b)carry-ripple vector merging,(c)combined carry-save and carry-ripple vector merging. 2021年2月 15
2021年2月 15 Vector merging Adder