GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 60

Answer 1

Answer : 3 (minimum Half adders required) 

Half adder contains 2 outputs ($Sum, Carry$) realized as $ Sum = A \bigoplus B $ and $ Carry = A  . B $

$f1$ and  $f4$ can be realized directly as providing C as another input (hence already consumes 3 Half adders)

now $f2$ and $f3$ should be in terms of XOR and AND‘s only, to covert we can expand A $\bigoplus$ B as

        $A \bigoplus B  = A’ .B + B’ . A$ 
 

now,

$f2  = A’.B.C + A.B’.C$

       $= (A’.B + A.B’). C $

       $= (A \bigoplus B  ).C$

which is one of the outputs of the already implemented Half adder (refer to diagram).

similarly,

$f3  = A.B.C’ + (A’+B’). C $

     $= (A.B). C’ + (A.B)’.C $

     $ = ((A.B) \bigoplus C )$

which is one of the other outputs of the already implemented half-adder (refer to diagram).

Implementation :

Comments

Sum = A XOR B , Carry = A.B

Answer 2

Circuit of a half-adder:

$3$ half-adders are enough to implement all $3$ functions simultaneously.