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Arithmetic II CPSC 321 E. J. Kim

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Today’s Menu Arithmetic-Logic Units Logic Design Revisited Faster Addition Multiplication (if time permits)
Goals We recall some basic logic gates Determine the  truth tables  for the Boolean functions We recall half-adders and full-adders Ripple-carry adders Discuss faster adders

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Logic Gates  AND gate  OR gate  NOT gate What are the truth tables?
Logic Gates  NOR gate  NAND gate  XOR gate What are the truth tables?

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Half Adder s c a b  a  b    c    s  0  0 0 0  0  1  0 1  1  0 0 1  1  1 1 0
Full Adder c in   a  b  c out s  0  0  0 0 0  0  0  1  0 1  0  1  0  0 1  0  1  1  1 0  1  0  0 0 1  1  0  1  1 0  1  1  0  1 0  1  1  1  1 1 Give a Boolean formula for s  s=cin xor a xor b Give a Boolean formula for  c out   c out  =ab+c in (a xor b) Design now a circuit using  and, or, xor.

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Full Adder c in a b c out s

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Critical Path c in a b c out s Suppose that each gate has a unit delay. What is the  critical path (= path with the longest delay)?
Ripple Carry Adders Each gates causes a delay

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This note was uploaded on 03/23/2011 for the course CPSC 350 taught by Professor Staff during the Spring '08 term at Texas A&M.

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slide6 - ArithmeticII CPSC321 E.J.Kim TodaysMenu...

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