Question

Is booth algorithm for multiplication only for multiplying 2 negative numbers (-3 * -4) or one positive and one negative number (-3 * 4) ? Whenever i multiply 2 positive numbers using booth algorithm i get a wrong result.

example : 5 * 4

A = 101 000 0 // binary of 5 is 101

S = 011 000 0 // 2's complement of 5 is 011

P = 000 100 0 // binary of 4 is 100

x = 3 number of bits in m

y = 3 number of bits in r

m = 5

-m = 2’s complement of m

r = 4

1. After right shift of P by 1 bit 0 000 100

2. After right shift of P by 1 bit 0 000 010

3. P+S = 011 001 0

   After right shift by 1 bit 0 011 001

4. Discarding the LSB 001100

   But that comes out to be the binary of 12 . It should have been 20(010100)

UPDATE after @ ruakh answer

5 * 4 = 20

m = 0101 is 5

r = 0100 is 4

A = 0101 0000 0

S = 1010 0000 0

P = 0000 0100 0

1. shift P right by 1 bit : 0 0000 0100

2. shift P right by 1 bit : 0 0000 0010

3. P+S = 10100010
   Shifting rightby 1 bit : 1101 0001

4. P+A = 1 0010 0001 here 1 is the carry generated
   shifting right by 1 bit : 110010000

Leave the LSB : 11001000 (not equal to 20)

Answer 1

You’re not giving enough room for your sign handling. 5 is not 101, but 0101: it has to start with a 0, because values starting with 1 are negative. 101 is actually -3: it’s the two’s complement of 011, which is 3. Similarly, 4 is not 100, but 0100; 100 is -4. So when you multiply 101 by 100, you’re actually multiplying -3 by -4; that’s why you get 12.