Details of Squaring Algorithm:What is squaring algorithm

Consider an integer n whose square is to be determined. Now if we know the square of , then we can easily compute the square of ‘n’. Here ‘n²’ can be written as,

                                           (4.13)                                                  

               (4.14)                                      

An integer X can be expressed as,

                                                  (4.15)

                                                                       

Now we consider. So X can be written as,

                                                                               (4.16)

                                                                       

                 (4.17)

                                               

                                                                              (4.18)

                                                                       

Illustration:- Consider the number X=”1110”=14₁₀ whose square is to be determined. X² can be represented as,

 

. Here, N=4. ‘1100’ can be represented as,

.  can be expressed as, .

So  can be represented as, .

 

 Flow chart of squaring algorithm shown in fig. 13. Variation of leakage power and time delay  with respect to input bits are shown in fig. 14 and fig. 15 respectively.

 

 

Fig(13)   Flow chart of squaring algorithm  

 

 

 

 

Fig.14.variation of leakage power

 

Fig.15.Performance graph of time delay