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Carry-Propagate AdderConnecting full-adders to make a multi-bit carry- Carry-Propagate AdderConnecting full-adders to make a multi-bit carry-

Carry-Propagate AdderConnecting full-adders to make a multi-bit carry- - PDF document

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Uploaded On 2016-02-28

Carry-Propagate AdderConnecting full-adders to make a multi-bit carry- - PPT Presentation

1 CarryLookAheadAddersBy precomputing the major part of each carry equation we can make a much faster adderWe start by computing the partial results for each bit 2 Now by forward substitution ID: 234761

1 Carry-LookAheadAddersBy pre-computing the major part

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1 Carry-Propagate AdderConnecting full-adders to make a multi-bit carry-propagate adder:Right-most adder adds least-significant bits. Carry-out is passed Carry-LookAheadAddersBy pre-computing the major part of each carry equation, we can make a much faster adder.We start by computing the partial results (for each bit): 2 Now, by forward substitution (show this and check for errors!)So we can express each carry as a function of generate andpropagate signals; in a two level AND-OR circuit and without any ripple effect!Carry-LookAheadAdders p/g generator (simple and/or gates) A3 B3 P1 G1 carry generator (a bit more complex butstill only AND/OR gates) C0 A0 B0 S0 A1 B1 S1 A2 B2 C2 A3 B3 C3 3 Hierarchical Carry-LookAheadAddersTheoretically, we could create a carry-lookaheadadder for any NBut these equations are complex. It is unreasonable to extendthis to beyond more than 4 bits or so. Why?Can combine carry look-ahead and carry-propagate schemes: Multipliers Consider a 1 bit x 1 bit multiplier:Multiplication of two bits is simply an AND gate 4 MultipliersOne bit number x N-bit numbereg. 10111011 x 1 = 1011101110111011 x 0 = 00000000 B(3:0)A x B(3:0) MultipliersN bit x N bit number (consider 4x4):This would require 16 AND gates and a 8 bit, 4 input adder,and lots of wiring (wiring is becoming a big problem inintegrated circuits). 5 MultipliersWe can reduce the wiring by distributing the adder: 2X3X2X1X0 S 30 7 MultipliersRecall: Half-Adder vs. Full-AdderBy combining half-adders, full-adders, and AND gates, we canimplement our array multiplier 6 Multipliers