BITS Assignment

Question

Use the Booth algorithm to multiply +21 (multiplicand) by -24 (multiplier), where each

number is represented using 6 bits.

 

I tried but I'm getting answers as 000100100111 which converts into 295 but 504 even in -504 form is 1000000111, so I'm not sure where am I going wrong. please answer it

Answer 1

(+21) = 010101

(-24) = (011000)’ + 1 = 101000

Here we are multiplying 6 bits x 6 bits, so the result will have a total of 12 bits (i.e 6 + 6)

(Reason: the multiplication of m bits x n bits gives a product which has (m+n) bits)

Therefore we extend the sign for each term (making each term 12 bits long),

Since +21 is a positive number, therefore extending 6 more zeros to it will give

(+21) = 000000 010101

and since -24 is a negative number, therefore extending 6 more ones, it will give:

(-24) = 111111 101000

Now, we convert the normal multiplier of (-24) to Booth multiplier and we get,

(-24) = 000000-11-1000

We can ignore the zeros at the beginning of Booth multiplier, so hence,

(-24) = -11-1000

Now we multiply:

000000 010101

x         -11-1000

Result: 100111111000001000

Now, we only need to first 12 bits from the LSB.

So the final answer become: 111000001000

Which is equal to -504

That’s it :)