Lecture 18

Lecture 18 - 1 ECE52 Spring 11 Lecture 18 2/23/11 Go...

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Unformatted text preview: 1 ECE52 Spring 11 Lecture 18 2/23/11 Go Beavers! 310 game conference losing streak shattered! 2/3 of the team M.E. or CompSci 2 The real magic comes from using cascaded levels of lookahead! Build basic blocks of size k bits, then use second level of lookahead circuits to determine carries between blocks. Much more efficient than brute- forcing large k! *if* we could build large fan-in gates with no speed penalty, large k CLA has constant 4 gate delay penalty (since is just a large 2-level AND-OR expression but of course not true! 1 1 1 2 1 2 1 1 1 ... ... ... c p p p p g p p p p g p p g p g c i i i i i i i i i i i----- + + + + + + = 3 32-bit adder from 4 8-bit CLA blocks Block x 31 24 c 32 c 24 y 31 24 s 31 24 x 15 8 c 16 y 15 8 s 15 8 c 8 x 7 y 7 s 7 c 3 Block 1 Block 4-stage ripple carry between blocks here 16 gate delays to generate 32-bit sum pretty good but we can do better! Note use of bus notation Book derives propagate, generate functions at block level ?! cares! who- 2011 cost. hardware increased much h albeit wit carry,- ripple for 65 vs numbers! bit - 32 2 add to delays gate total 8 inputs, 8 n larger tha gate no etc. , for similarly ... 1 2 3 1 2 3 1 2 3 2 3 3 32 1 2 1 2 1 2 2 24 1 1 1 8 1 1 16 8 2 2 1 1 1 2 3 4 5 6 7 5 6 7 6 7 7 1 2 3 4 5 6 7 c P P P P G P P P G P P G P G c c P P P G P P G P G c c P P G P G c P G c c P G c ,G ,P ,G P g p p p p p p p g p p g p g G p p p p p p p p P + + + + = + + + = + + = + = + = + + + + = = 5 Figure 5.18. A hierarchical carry-lookahead adder.A hierarchical carry-lookahead adder....
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Lecture 18 - 1 ECE52 Spring 11 Lecture 18 2/23/11 Go...

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