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Unformatted text preview: Building Blocks For Arithmetic Binary Addition: recall the fulladder design. a b s FA carry sum s b a ( ab + a b ) s + ( ab + a b ) s ab + a b ab + as + bs Integer Addition Fulladder: Three input bits a , b , s Output: two bits sum and carry Logic equations and gate diagram derived from truthtables. What about 4bit addition? Integer Addition Solution 1: write truthtable, derive logic equations, draw gate diagram. Solution 2: 1 1 1 1 + 0 1 1 1 1 0 0 0 1 Use a number of fulladders! Integer Addition leastsignificant FA FA FA FA 1 1 1 1 1 1 1 1 bit: set carryin to 0 carryout of one stage is the carryin for the next 1 2's complement? Addition time for N bits? Integer Addition Observation: all we need is the carryout... compute carryout cout for blocks input: 0 0, cout = 0 kill input: 1 1, cout = 1 generate input: 0 1 or 1 0, cout =carryin ( cin ) propagate cout = cin P + G G = a b P = a + b Block codes: G 01 = G 1 + G P 1 P 01 = P P 1 Integer Addition...
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 Spring '07
 MCKEE/LONG

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