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. multiplicand:

Answer 1

To determine the product of two binary numbers using Booth's algorithm, we follow specific steps involving shifts, additions, and subtractions. In this case, we determine the product of a = (1111 1110)2 and b = (0001 0000)2.

Step-by-step explanation:

In Booth's algorithm, we multiply binary numbers using shifts, additions, and subtractions. To determine axb, we start with a multiplicand (b) and a multiplier (a) in binary form. Then, we follow the steps of Booth's algorithm:

1. Set up a product register and initialize it to 0.
2. Add a sign bit to the least significant end of the product register, making it 9 bits long.
3. Initialize the multiplication counter to the number of bits in the multiplier (4 in this case).
4. Loop through the following steps:
   1. If the last two bits of the multiplier are '10' or '01', perform a subtraction of the multiplicand from the product register.
   2. If the last two bits of the multiplier are '00', ignore this step.
   3. If the last two bits of the multiplier are '11', perform an addition of the multiplicand to the product register.
   4. Right shift the multiplier by 1 bit.
   5. Right shift the product register by 1 bit, and store the shifted out bit for complementing in the next step.
   6. If the shifted out bit was '1', complement the product register.
   7. Decrement the multiplication counter by 1.

Following these steps, we can determine the product of a = (1111 1110)2 and b = (0001 0000)2 using Booth's algorithm.