Compute the sum and product of 101112 and 111002 while stayi

Compute the sum and product of (10111)_2 and (11100)_2, while staying in the binary system. For the sum, count the number of bit additions that are required.

Solution

The rules for binary addition includes

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10 (which is 0 carry 1)

Let us take these and add given numbers

1 0 1 1 1

1 1 1 0 0

+

1 0 0 1 1 (now here starting from right most bit 1+0 is 1, then next is 1+0 which is 1, then 1+1 which is 10(written as 0 and carry 1, now this carry goes to next bit and makes it 1+1 again 0 and carrry 1 then goes to next 1+1 with carry 1 , which makes it 1)

Multiplication of binary number and rules it uses are

0 x 0 = 0

1 x 0 = 0

1 x 1 = 1

Let us see multiplication of 10111 and 11100

Answer is 001100100

				1	0	1	1	1
				1	1	1	0	0
				0	0	0	0	0
			0	0	0	0	0	X
		1	0	1	1	1	X	X
	1	0	1	1	1	X	X	X
1	0	1	1	1	X	X	X	X
0	0	1	1	0	0	1	0	0