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What is the Booth’s coding in 8-bits for an integer (-86)?
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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

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