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If only half adder used for addition then the number of half adders required to add two 'm' bit numbers is;

A) 2m-1

B) 2m-1

C) 2m+1


in Digital Logic 2.5k views

3 Answers

0 votes
To realize a Full adder we need two half adders.

Now to add 2 m bit no.s we need m-1 full adders and the LSB bit addition requires a half adder.

So, no. of half adders needed= 2*(m-1) +1 =2m-2+1=2m-1
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With the help of 2 Half-Adder and 1 OR gate, we can build 1 full adder.
To add two m bits we need (m-1) F.A and 1 H.A
To construct  (m-1) FA we need 2(m-1) = 2m -2 Half adders 

So, to add two m bits, we need total 2m-2 +1 = 2m -1 Half adders 
(A) is correct option!

0 votes
Actually in question they said that we have only half adders so as to implement a full adder we need two half adder and one OR gate ,that OR gate should also be implemented using half adder only and to implement one OR gate we need two half adder so overall to implement one full adder we need only 4 half adders.
Now, to implement (m-1) full adder we need 4*(m-1) half adders.
Therefore,to add two m bit numbers we need total 4*(m-1)+1=4m-3 half adders.
Thus all options are incorrect.

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