Question

`1) How is -9 (base 10) represented in 8-bit two's complement notation?

a) 00001001

b)11110111

c)11110110

d) 11111001

2) The binary addition of 1 + 1 + 1 + 1 =

A) 1111(base 2)

b) 0001(base2)

C) 0100(base2)

D) 1001(base2)

3) How is –1 (base 10) represented in 8-bit two's complement notation?

A) 1111111-

B) 111111111

C) 00000001

D) 00000010

Answer 1

Answer:
--------
1)  b.  11110111
2)  c.  0100(base2)
3)  11111111

Explanation:
-------------
1)
This is negative. so, follow these steps to convert this into a 2's complement binary
Step 1:
Divide 9 successively by 2 until the quotient 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 1001
So, 9 of decimal is 1001 in binary
Adding 4 zeros on left hand side of this number to make this of length 8
So, 9 in normal binary is 00001001
Step 2: flip all the bits. Flip all 0's to 1 and all 1's to 0.
   00001001 is flipped to 11110110
Step 3:. Add 1 to above result
11110110 + 1 = 11110111
so, -9 in 2's complement binary is 11110111

2)
1+1+1+1 = 4
Divide 4 successively by 2 until the quotient is 0
   > 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 100
So, 4 of decimal is 100 in binary
Answer: 0100

3)
This is negative. so, follow these steps to convert this into a 2's complement binary
Step 1:
Divide 1 successively by 2 until the quotient is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1
So, 1 of decimal is 1 in binary
Adding 7 zeros on left hand side of this number to make this of length 8
So, 1 in normal binary is 00000001
Step 2: flip all the bits. Flip all 0's to 1 and all 1's to 0.
   00000001 is flipped to 11111110
Step 3:. Add 1 to above result
11111110 + 1 = 11111111
so, -1 in 2's complement binary is 11111111