# Booth bit-pair recoding of multipliers doubt

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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 0 0 +1 0 -1 +1 -2 +1 +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?

## Related questions

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Let's say we have a multiplier $(10101010)_2$. Then applying booth re-coding, Method 1: appending a zero at the end: $(1\ 0\ 1\ 0\ 1\ 0\ 1\ 0\ 0)_2 => (-1\ 1\ -1\ 1\ -1\ 1\ -1\ 0)_2$ Method 2: without appending a ... is the following condition true? #multiplier bits must be equal to #multiplicand bits Please don't give any ref link because I've already searched but didn't got my doubt cleared.
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