Question

Design a digital system that multiplies two unsigned binary numbers using the repeated addition method. For example, to multiply 5 by 4, the digital system adds the multiplicand four times (5 + 5 + 5 + 5). This method is known as:

a) Booth's algorithm
b) Division method
c) Karatsuba algorithm
d) Addition-Subtraction method

Answer 1

The repeated addition method for multiplying two unsigned binary numbers is not specifically named by any of the listed algorithms but is a conceptual approach involving adding the multiplicand to itself as many times as specified by the multiplier.

Step-by-step explanation:

The digital system that multiplies two unsigned binary numbers using the repeated addition method is not directly represented by any of the algorithms listed (Booth's algorithm, Division method, Karatsuba algorithm, Addition-Subtraction method). The repeated addition method is a basic multiplication technique that involves adding the multiplicand to itself multiple times, equivalent to the number of the multiplier.

For multiplication of unsigned binary numbers using the repeated addition method, the digital system would require an adder to perform the addition and a counter to track the number of additions. If you were to multiply 5 by 4, you would initialize a sum to 0, and repeatedly add 5 to this sum four times. After four additions, the sum would equal 20, which is the product of 5 and 4.

This approach is fundamental and not as efficient as advanced multiplication algorithms, but it is conceptually simple and suitable for learning purposes. More sophisticated methods, like Booth's algorithm, are designed to optimize the multiplication process and are more commonly used in actual hardware implementations.