Question

Problem: Perform following operations in binary using 8-bit addition/subtraction/multiplication.
1. −80 + 42
2. −99 − 20
3. 60 − 70
4. −59 × 3
5. 52×−1

Answer 1

I am providing Solution using 2's complement.

2's Complement of a binary number is " Adding 1 to 1's compliment of that number" and, 1's complement of a binary no. obtained by converting digits 0 to 1 and 1 to 0.

ADDITION / SUBTRACTION

1.)

80 in binary is = 01010000 and 42 is = 00101010

-80 = (1's compliment of 80 )+ 1

So, -80= (10101111) +1 = 10110000

now, -80 + 42 = (10110000) + (00101010) = 11011010

Here 8^th bit of Sum is 1 so, number is negative.

So, to find the magnitude of no, we have to find its 2’s complement.

So, 2’s complement of 11011010= 00100101 +1 = 00100110 = 38

and though, number is negative, hence, answer is -38

2.)

99= 01100011

-99= 10011100 + 1= 10011101

20= 00010100

-20= 11101011 + 1= 11101100

So, -99 + -20 = (10011101) + (11101100) = 10001001

Here 8^th bit of Sum is 1 so, number is negative.

So, to find the magnitude of no, we have to find its 2’s complement.

So, 2’s complement of 10001001= 01110110 +1 = 01110111= 119

and though, number is negative, hence, answer is -119

3.)

60= 00111100

70= 01000110

-70= 10111001+ 1= 10111010

So, 60+ (-70) = (00111100) + (10111010) = 11110110

Here 8^th bit of Sum is 1 so, number is negative.

So, to find the magnitude of no, we have to find its 2’s complement.

So, 2’s complement of 11110110= 00001001 +1 = 00001010= 10

and though, number is negative, hence, answer is -10

MULTIPLICATION

5.)

52= 00110100

1= 00000001

-1= 11111110+ 1=11111111

doing normal binary multiplication of (00110100) and (11111111)

So, Output is 11001100

Here 8^th bit of Sum is 1 so, number is negative.

So, to find the magnitude of no, we have to find its 2’s complement.

So, 2’s complement of 11001100= 00110011 +1 = 00110100= 52

and though, numberis negative, hence, answer is -52

I hope, this solution will help you. If You still have doubt about 2's compliment or addition/subtraction/multiplication, you can put your doubts in comment section. I would like to sort them out. THANK YOU!