no need to remember the table...
here's the logic simplified==>
just 1 example is enough..
lets take 101
check pairs consecutively
we have 10 and 01.
do (right bit - left bit) for each pair
meaning (0-1) and (1-0) i.e. -1 and 1
now interpret -1,1 as a weighted binary number
i.e. -1*2^1 + 1*2^0 = -2+1 = -1
check table 101 is -1
now multiply Y ..👍🏻👍🏻
generalising----------
1 bit recording for 1010 is (0-1)(1-0)(0-1) i.e. -11-1
2 bit recording for 1010 is -11
3 bit recording for 1010 is -3