Question

Suppose a = (1111 1110)2 and b = (0001 0000)2. Determine axb using Booth's algorithm if a is the multiplier and b is the multiplicand.

Fill in the blanks: The result of axb using Booth's algorithm is ____________.

Answer 1

Booth's algorithm is used to multiply binary numbers. The result of axb is (-)(1111 0110)2.

Step-by-step explanation:

Booth's algorithm is used for multiplying binary numbers. In this case, we have a = (1111 1110)2 and b = (0001 0000)2. To find the product axb using Booth's algorithm, we perform the following steps:

1. Extend the sign of a to the left by copying the sign bit. This gives us (-)(1111 1110).2
2. Since b is positive, we can directly use it for multiplication.
3. Perform the multiplication:

• Shift b one bit to the right and add a to the result:
• (0000 1000)2 + (-)(1111 1110)2 = (-)(1111 0110)2

Therefore, the result of axb using Booth's algorithm is (-)(1111 0110)2