Day3_6up

Day3_6up - 1 Penn ESE534 Spring2010 -- DeHon 1 ESE534:...

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Unformatted text preview: 1 Penn ESE534 Spring2010 -- DeHon 1 ESE534: Computer Organization Day 3: January 25, 2010 Arithmetic Work preclass exercise Penn ESE534 Spring2010 -- DeHon 2 Last Time Boolean logic computing any finite function Saw gatesand a few properties of logic Penn ESE534 Spring2010 -- DeHon 3 Today Addition organization design space parallel prefix Penn ESE534 Spring2010 -- DeHon 4 Why? Start getting a handle on Complexity Area and time Area-time tradeoffs Parallelism Regularity Arithmetic underlies much computation grounds out complexity Preclass Penn ESE534 Spring2010 -- DeHon 5 Circuit 1 Can the delay be reduced? How? To what? Penn ESE534 Spring2010 -- DeHon 6 2 Tree Reduce AND Penn ESE534 Spring2010 -- DeHon 7 Circuit 2 Can the delay be reduced? Penn ESE534 Spring2010 -- DeHon 8 Circuit 3 Can the delay be reduced? Penn ESE534 Spring2010 -- DeHon 9 Brute Force Multi-Output AND How big? ~38 here in general about N 2 /2 Penn ESE534 Spring2010 -- DeHon 10 Brute Force Multi-Output AND Can we do better? Penn ESE534 Spring2010 -- DeHon 11 Circuit 4 Can the delay be reduced? Penn ESE534 Spring2010 -- DeHon 12 3 Addition Penn ESE534 Spring2010 -- DeHon 13 Penn ESE534 Spring2010 -- DeHon 14 C: 00 A: 01101101010 B: 01100101100 S: 0 C: 000 A: 01101101010 B: 01100101100 S: 10 C: 0000 A: 01101101010 B: 01100101100 S: 110 C: 10000 A: 01101101010 B: 01100101100 S: 0110 C: 010000 A: 01101101010 B: 01100101100 S: 10110 C: 1010000 A: 01101101010 B: 01100101100 S: 010110 C: 11010000 A: 01101101010 B: 01100101100 S: 0010110 C: 011010000 A: 01101101010 B: 01100101100 S: 10010110 C: 1011010000 A: 01101101010 B: 01100101100 S: 010010110 C: 11011010000 A: 01101101010 B: 01100101100 S: 1010010110 C: 11011010000 A: 01101101010 B: 01100101100 S: 11010010110 Example: Bit Level Addition Addition Base 2 example A: 01101101010 B: 01100101100 S: C: 0 A: 01101101010 B: 01100101100 S: Penn ESE534 Spring2010 -- DeHon 15 Addition Base 2 A = a n-1 *2 (n-1) +a n-2 *2 (n-2) +... a 1 *2 1 + a *2 = (a i *2 i ) S=A+B What is the function for s i carry i ?...
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Day3_6up - 1 Penn ESE534 Spring2010 -- DeHon 1 ESE534:...

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