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UPPCL AE 2018:68

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Which of the following circuits are equivalent (i.e., they produce the same output for all inputs)?

$\text{F} = ab + bc + ca$

$\text{G} = (a+b)(b+c)(c+a)$

$\text{H} = \text{NAND(NAND(a,b), NAND(b,c),NAND(c,a))} $

  1. $\text{F}$ and $\text{H}$
  2. $\text{F}$ and $\text{G}$
  3. $\text{F, G}$ and $\text{H}$
  4. $\text{G}$ and $\text{H}$
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F = ab + bc + ca

 

G = (a + b)(b + c)(c + a)

   =  (b + ac)(c + a)                                                                    Distributive Law [ (x+y)(x+z) = x + yz]

   =  bc + ba + ac*c +ac*c

   =  bc+ ba +ac +ac

   =  ab + bc + ca

NAND- NAND Realization is Equivalent to AND-OR Realization.

H =  NAND [NAND(a,b), NAND(b,c), NAND(c,a)]

    =  OR[AND(a,b), AND(b,c), AND(c,a)]

    =  OR[ab, bc, ca]

    =   ab + bc + ca 

So, F,G,H are Equivalent.

        

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