Booth's encoding is used to fasten the process of multiplication . Here we need that the multiplier is encoded to Booth's encoding form first and then we do multiplication .
Given a 2-s complement representation of a number we convert into Booth's encoding form as according to rules mentioned below :
a) If ith bit is '1' and (i-1)th bit is '0' , we substitute ith bit with '-1' .
b) If ith bit is '0' and (i-1)th bit is '1' , we substitute ith bit with '+1' .
c) If ith bit is '0' and (i-1)th bit is '0' or ith bit is '1' and (i-1)th bit is '1' then , we substitute ith bit with '0'.
d) If LSB bit a0 is '1' , we assume that a-1 is there and = '0' and hence substitute it with '-1' .
So we write the 2's complement representation of the given number first and then do Booth's encoding on it.
So 2's complement representation of -86 = 10101010
Hence performing the above mentioned rules , we obtain :
2's complement number : 1 --> 0 --> 1 --> 0 --> 1 --> 0 --> 1 --> 0
Booth's encoding : -1 +1 -1 +1 -1 +1 -1 0
Hence the required Booth's encoding of -86 : -1 +1 -1 +1 -1 +1 -1 0