l11 - Building Blocks For Arithmetic Binary Addition:...

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Unformatted text preview: Building Blocks For Arithmetic Binary Addition: recall the full-adder 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 Full-adder: Three input bits a , b , s Output: two bits sum and carry Logic equations and gate diagram derived from truth-tables. What about 4-bit addition? Integer Addition Solution 1: write truth-table, 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 full-adders! Integer Addition least-significant FA FA FA FA 1 1 1 1 1 1 1 1 bit: set carry-in to 0 carry-out of one stage is the carry-in for the next 1 2's complement? Addition time for N bits? Integer Addition Observation: all we need is the carry-out... compute carry-out cout for blocks input: 0 0, cout = 0 kill input: 1 1, cout = 1 generate input: 0 1 or 1 0, cout =carry-in ( 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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l11 - Building Blocks For Arithmetic Binary Addition:...

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