57 in 2's compliment form = 11000111
So Q=11000111, q(_1 in suffix)=0
We know in bit pairs 00 and 11= ASR, 01=+,ASR , 10=-,ASR
So now Q q_1
11000111 0
from right to left bit pair in reverse order (10)(11)(11)(01)(00)(00)(10)(11)
so booth coding for 8 bit decimal number -57 is ------
step 1= -(1^0) (1^1) (1^1) +(0^1) (0^0) (0^0) -(1^0) (1^1)
step 2= - 1 0 0 + 1 0 0 - 1 0
step 3=reverse it= 0 - 1 0 0 + 1 0 0 - 1