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Updated on March 29, 2024

Booth’s Algorithm Multiplication Calculator

Booth’s Algorithm is a method used for multiplying two binary numbers efficiently. This algorithm is often used in computer processors for fast multiplication operations. In this article, we will discuss Booth’s Algorithm in detail and provide a calculator tool to help you understand how it works.

Booth’s Algorithm Multiplication Calculator

Multiplier (M):
Multiplier Length:
Multiplier Sign Bit:
Multiplier Bits:
Multiplier Shifted:
Product Register:
Product Accumulator:
Booth Control:

Understanding Booth’s Algorithm

Booth’s Algorithm is a multiplication algorithm that allows for efficient multiplication of two binary numbers by using a technique called “the recoding of binary numbers.” The algorithm helps reduce the number of operations required for multiplication by examining groups of consecutive bits in the multiplier. By analyzing these bit groups, the algorithm can determine when to add, subtract, or shift the partial products.

The key idea behind Booth’s Algorithm is to replace groups of bits in the multiplier with a recoded version that has fewer bits. This recoding process helps in reducing the number of operations required during multiplication, making it more efficient than traditional methods.


How Booth’s Algorithm Works

Booth’s Algorithm works by examining pairs of bits in the multiplier and using them to determine the appropriate operation to be performed. The algorithm starts by initializing a product register with the multiplicand and a separate accumulator register with zeros. It then proceeds to scan the multiplier from right to left, examining pairs of bits at a time.

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Based on the values of the current bit pair and the previous bit pair, the algorithm decides whether to add, subtract, or shift the partial product. The process continues until all the bits in the multiplier have been processed. At the end of the algorithm, the product register contains the final result of the multiplication operation.

Booth’s Algorithm Multiplication Calculator

To better understand how Booth’s Algorithm works, we have provided a calculator tool that allows you to input two binary numbers and see the step-by-step process of multiplication using Booth’s Algorithm. Simply enter the multiplicand and multiplier in binary form, and the calculator will show you the intermediate steps involved in the multiplication process.

Benefits of Using Booth’s Algorithm

There are several advantages to using Booth’s Algorithm for multiplication:

  • Efficiency: Booth’s Algorithm reduces the number of operations required for multiplication, making it faster than traditional methods.
  • Hardware Implementation: The algorithm is well-suited for implementation in hardware, making it ideal for computer processors.
  • Accuracy: Booth’s Algorithm provides accurate results for binary multiplication operations.


Booth’s Algorithm is a powerful method for multiplying binary numbers efficiently. By understanding the principles behind the algorithm and using the provided calculator tool, you can gain a better insight into how it works and its benefits. Whether you are a student learning about computer algorithms or a professional working with processors, Booth’s Algorithm is a valuable tool to have in your arsenal.