Multiply (-13)×(-20) using Booths Algorithm.

Welcome to our channel! In today's video, we'll dive into Booth's Algorithm, a powerful technique for binary multiplication, especially useful for two's complement numbers. Let's break it down step by step!

Introduction:

Brief overview of binary multiplication.

Introduction to Booth's Algorithm and its advantages, especially in handling signed numbers.

Step-by-Step Explanation:

Initialize Variables:

Multiplicand (M)

Multiplier (Q)

Accumulator (A): Start with 0.

Q-1: An additional bit initialized to 0.

Count: Number of bits in the multiplier.

Main Loop:

Repeat for the number of bits in the multiplier:

Check Last Two Bits (Q₀ and Q-1):

If the pair is 10: Subtract M from A.

If the pair is 01: Add M to A.

Arithmetic Shift Right (ASR):

Shift the combined AQ and Q-1 right by one bit.

Maintain the sign bit of A.

End Condition:

After all bits are processed, A and Q together form the final product.

Example Walkthrough:

Demonstrate the algorithm with a simple example:

Multiplicand (M) = 3 (0011)

Multiplier (Q) = -4 (1100 in two's complement)

Walk through each iteration showing the changes in A, Q, and Q-1.

Benefits of Booth's Algorithm:

Efficient handling of positive and negative multipliers.

Reduces the number of required addition/subtraction operations.

Conclusion:

Recap the process.

Highlight practical applications in computer arithmetic and digital signal processing.