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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?

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