# Booth bit-pair recoding of multipliers

1) In Booth's bit-pair recording technique how to multiply a multiplicand with 2?

2) In booth's algorithm for multiplication/Booth's bit-pair recording of multipliers, the sign bit extension of the multiplicand i.e. we must extend the sign-bit value of the multiplicand to the left as far as the product will extend. Now my question is what should be the value of extended Sign Bit?

I think following are the possible values-

Multiplier Bit, Extended sign bit value

i) 0, 0

ii) +1, 0

iii) -1, 1

iv) -2, 1

v) 2, I don't know

Also, why is the sign bit extended? Will we get the correct answer if we don't extend sign bit?