Two - Bit Binary Multiplier

Ask

A 2 bit binary multiplier can be implemented using

(a)2 input ANDs only

(b)2 input X-ORs and 2-input AND gates only

(c)Two (2) input NORs and one XNOR gate

(d) XOR gates and shift registers

Think

Binary Multiplier !?! I know very little about Binary Multiplication ...May be like , 10 $\times$ 11 =  110

Concept

Yes, it's as simple as that !Let's see an Example for Binary Multiplication :
          1 1 0 0
       $\times$ 1  1
____________
          1 1 0  0
                                    1 1 0 0
                            ____________
                                    1 0 1 0  0




To  start with the  2- bit binary multiplier
Consider the input as $A_0 B_0$ & $A_1, B_1$. This gives a 4-bit product.$P_0, P_1 , P_2,P_3$
Just, take a look at the schematic below:

 

Concept

    From the above, it is evident
    $P_0 = A_0A_1$
    $P_1 = B_0A_1 + B1A_0$ $\implies$ Carry $C_1$ from here is  cascaded  to  $P_2$  
    $P_2 = B_0B_1  + C_1$  $\implies$ Carry $C_2$ from here is  cascaded to $P_3$
    $P_3 = C_2$
                              As we can see there are only two quantities being added , this means that only a TWO input Adder is sufficient.A HALF - ADDER does this job.

Focus

 So, now we realize the above multiplication , using the below schematic :

Schematic Realization of 2-bit multiplier using Half- Adders (HA)

            While we all know the realization of a HALF- ADDER is done using 2-input AND gate & 2-input Ex-OR gate. To know more about Half Adder please click here.
Below is a schematic of a  HALF- ADDER:

Focus

Add caption

There by , we could conclude that the correct answer is (b)