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EXTRACTING SQUARE ROOT FROM BINARY NUMBER:

Here the binary number is 110010101(decimal equivalent 405) .The square root of this number is extracted in the following way.

First the number is grouped in pairs from LSB .Thus only ‘1’ is left. Nearest square of ‘1’ is 1. Twice of 1 is ‘10’. We get remainder ‘0’.

Here N=01. Now N is less than 10 so we put the result as 0. Remainder R=01-10*0=1.

Here N=10. Subtracting duplex from10 we get 10-02 =10.Nearest multiple of 10 is1. So the result is 1. Remainder R=10-10*1=0.

Here N=00. Duplex =10(0*1) = 0. Subtracting duplex from N, N=00-00 =00. R =00-10*0= 0 i.e result becomes 0.

N=01. Duplex = 10(0*0) +12  =1.  Subtracting duplex from N, N = 01- 1= 0. R = 00-10*0 = 00 i.e. 0 is stored in resultant part.

N= 00. Duplex = 10(0*0)+10(1*0)=0. Subtracting duplex from N, N=00-0 =0. R =00 -10*0 =0 i.e. 0 is stored.

N=01. Duplex = 10(0*0) +10(1*0) + 02=00. Subtracting duplex from N, N=01-00=01. R=01-10*0= 01 i.e. 0 is stored.

N=10. Duplex=10(0*0)+10(1*0)+10(0*0)=0. Subtracting duplex N=10-00=10. R= 10-10*1=0 i.e. 1 is stored in resultant part.

N=01. Duplex= 10(0*1) +10(1*0) +10(0*0) +02=00. Subtracting duplex from N=01-00=01. R=01-10*0=01 i.e.  0 is stored in resultant part.

Computed square root (in decimal) =20.125.

Actual value = 20.1246118.