Booth’s algorithm is a multiplication algorithm used for binary numbers.

- It is not directly applicable to decimal numbers like +5 and -15.
- However, we can convert these decimal numbers to their binary representations and then apply Booth’s algorithm.

## Let’s convert +5 and -15 to their binary representations:

+5 = 0101

-15 = 1111 (two’s complement representation)

Now, let’s perform the multiplication using Booth’s algorithm.

## Step 1: Set up the variables

A = 0101 (binary representation of +5)

B = 1111 (binary representation of -15)

Q = 0000 (accumulator for the result)

Q(-1) = 0 (previous value of the least significant bit of Q)

M = 4 (number of bits in the binary representation)

## Step 2: Perform the multiplication using Booth’s algorithm

Step | Operation | A | Q | Q(-1) |

0 | Initial values | 0101 | 0000 | 0 |

1 | A = A – B | 0101 | 0000 | 0 |

2 | Right Shift | 0010 | 1000 | 0 |

3 | A = A + B | 0111 | 1000 | 0 |

4 | Right Shift | 0011 | 1100 | 0 |

5 | A = A + B | 1011 | 1100 | 0 |

6 | Right Shift | 1101 | 1110 | 0 |

7 | A = A + B | 0011 | 1110 | 0 |

8 | Right Shift | 0001 | 1111 | 1 |

9 | A = A + B | 1111 | 1111 | 1 |

10 | Right Shift | 1111 | 1111 | 1 |

The final result is Q = 1111 (binary), which is equal to -15 in decimal notation.

Therefore, the result of multiplying +5 and -15 using Booth’s algorithm is -15.