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Login NowBooth algorithm gives a procedure for multiplying binary integers in signed 2’s complement notation

__Hardware Implementation:__

- Here, sign bit are not separated
- Registers A, B and Q are renamed to AC, BR and QR
- Extra flip-flop Q
_{n+1}is appended to QR which stores almost lost right shifted bit of the multiplier. - Pair Q
_{n}Q_{n+1}inspect double bits of the multiplier

**Problem****:**

Solution:

Multiplication (M) = (-4)_{10} = 1100

Multiplication (-M) = (+4)_{10} = 0100

Q = (-3)_{10} = 1101

Now,

Steps |
AC |
Q |
Q_{n-1} |
Operation |

0000 | 1101 | 0 | Initial | |

1^{st} |
0100 | 1100 | 0 | AC = AC – M |

0010 | 0110 | 1 | Right Shift | |

2^{nd} |
1110 | 0110 | 1 | AC = Ac + M |

1111 | 0011 | 0 | Right Shift | |

3^{rd} |
0011 | 0011 | 0 | AC = AC – M |

0001 | 1001 | 1 | Right Shift | |

4^{th} |
0000 | 1100 | 1 | Right Shift |

Hence,

Result = AC and Q

i.e. 0000 1100

Therefore, Result = (-4)_{10} x (-3)_{10} = (12)_{10}

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