Question

Show the representation of the following values in 8-bit two's complement notation:

15

-75

-3

109

Answer 1

1)
Since this is a positive number. we can directly convert this into binary
Divide 15 successively by 2 until the quotient is 0
   > 15/2 = 7, remainder is 1
   > 7/2 = 3, remainder is 1
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1111
So, 15 of decimal is 1111 in binary
Adding 4 zeros on left hand side of this number to make this of length 8
so, 15 in 2's complement binary is 00001111
Answer: 00001111

2)
This is negative. so, follow these steps to convert this into a 2's complement binary
Step 1:
Divide 75 successively by 2 until the quotient is 0
   > 75/2 = 37, remainder is 1
   > 37/2 = 18, remainder is 1
   > 18/2 = 9, remainder is 0
   > 9/2 = 4, remainder is 1
   > 4/2 = 2, remainder is 0
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1001011
So, 75 of decimal is 1001011 in binary
Adding 1 zeros on left hand side of this number to make this of length 8
So, 75 in normal binary is 01001011
Step 2: flip all the bits. Flip all 0's to 1 and all 1's to 0.
   01001011 is flipped to 10110100
Step 3:. Add 1 to above result
10110100 + 1 = 10110101
so, -75 in 2's complement binary is 10110101
Answer: 10110101

3)
This is negative. so, follow these steps to convert this into a 2's complement binary
Step 1:
Divide 3 successively by 2 until the quotient is 0
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 11
So, 3 of decimal is 11 in binary
Adding 6 zeros on left hand side of this number to make this of length 8
So, 3 in normal binary is 00000011
Step 2: flip all the bits. Flip all 0's to 1 and all 1's to 0.
   00000011 is flipped to 11111100
Step 3:. Add 1 to above result
11111100 + 1 = 11111101
so, -3 in 2's complement binary is 11111101
Answer: 11111101

4)
Since this is a positive number. we can directly convert this into binary
Divide 109 successively by 2 until the quotient is 0
   > 109/2 = 54, remainder is 1
   > 54/2 = 27, remainder is 0
   > 27/2 = 13, remainder is 1
   > 13/2 = 6, remainder is 1
   > 6/2 = 3, remainder is 0
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1101101
So, 109 of decimal is 1101101 in binary
Adding 1 zeros on left hand side of this number to make this of length 8
so, 109 in 2's complement binary is 01101101
Answer: 01101101