Carry+Lookahead+Addition (1)

Carry+Lookahead+Addition (1) - EECS 270 Carry Lookahead...

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UM EECS 270 Fall 2009 EECS 270 Carry Lookahead Addition
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UM EECS 270 Fall 2009 Half and Full adder Half Adder A B S C A B 0 0 1 1 0 1 0 1 0 1 1 0 S 0 0 0 1 C Full Adder A B C 0 S 1
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UM EECS 270 Fall 2009 8-bit Ripple Carry Adder Full adder C A 7 B 7 A 6 B 6 A 5 B 5 A 4 B 4 A 3 B 3 A 2 B 2 A 1 B 1 A 0 B 0 Full adder Full adder Full adder Full adder Full adder Full adder Full adder S 7 S 2 S 1 S 0 S 6 S 5 S 4 S 3 Carry Unfortunately this has a very large propagation time for 32 or 64 bit addition
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UM EECS 270 Fall 2009
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UM EECS 270 Fall 2009 Single Bit Carry Generate Generate: Do these two bits generate a carry? No No Yes No 0 0 ? 0 1 ? 1 0 ? 1 1 ? g i = a i b i a i b i
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UM EECS 270 Fall 2009 Single Bit Carry Propagate No 0 0 ? Yes 0 1 ? Yes 1 0 ? Yes 1 1 ? Propagate: Do these two bits let a carry-in propagate? a i b i p i = a i + b i
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UM EECS 270 Fall 2009 Generate for Bit Ranges G i+ 1 ,i = g i+1 + ( g i p i+ 1 ) i i + 1 a i+ 1 b i+ 1 a i b i ? G i+m+ 1 +n, i = G i+m+ 1 +n, i+m+ 1 + ( G i+m, i P i+m+ 1 +n, i+m+ 1 ) ? i i+ m+ 1 i+m i+m+ 1+n m -bit range n -bit range
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Propagate for Bit Ranges i i + 1 a i+1 b i+1 a i b i ? P
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This note was uploaded on 04/18/2011 for the course EECS 270 taught by Professor David during the Spring '11 term at Michigan State University.

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Carry+Lookahead+Addition (1) - EECS 270 Carry Lookahead...

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