TestBook Test Series: Digital Logic - Digital Circuits

Question

Let X be the number of AND gates required and Y be the number of OR gates required in 4-bit Carry lookahead adder . Then what is value of 2X+2Y?

My doubt here is they are just talking about AND and OR gate but usually we use AND,OR as well as XOR gate in CLA adder,

Do we need to expand XOR gate and consider the AND and OR gate?

Please Explain ?

Comments

Only AND and OR gates are to be considered.

Answer 1

See there are 3 steps to this :

a) Before entering into CLA circuit , n AND gates and n XOR gates for generator and propogator functions required for a_i and b_i operand values..

b) In the CLA circuit , we have 2 level implementation of AND gates followed by OR gates :

So in that no of AND gates required  = n(n+1) / 2

And no of OR gates   =   n

Therefore for 4 bit carrylookahead adder ,

No of AND gates in total required = 4 + (4*5/2)

                                                = 14

No of OR gates                         =  4

Therefore   2X  = 2*14  = 28

   and        2Y  =  2*4   =  8

So 2X + 2Y  = 28 + 8  

                   = 36

Hence 36 is the correct answer..

Comments

shouldn't we consider that outer n AND gates which you said in step one ?

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Ya I have considered that..

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Ya i mistaken it sorry