Question

convert -99 into 8-bit sign-magnitude, 1's complement, 2's complement.

show detailed explanations for all conversions.

Answer 1

-99
------
This is negative. so, follow these steps to convert this to various binary formats.
Divide 99 successively by 2 until the quotient is 0
   > 99/2 = 49, remainder is 1
   > 49/2 = 24, remainder is 1
   > 24/2 = 12, remainder is 0
   > 12/2 = 6, remainder is 0
   > 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 1100011
So, 99 of decimal is 1100011 in binary
Adding 1 zeros on left hand side of this number to make this of length 8
So, 99 in normal binary format is 01100011
sign-magnitude:
-----------------
set 1 as left most bit, since this number is negative.
so, 01100011 becomes 11100011
=====================================
||    sign-magnitude: 11100011    ||
=====================================

1's complement:
-----------------
flip all the bits. Flip all 0's to 1 and all 1's to 0.
   01100011 is flipped to 10011100
=====================================
||    1's complement: 10011100    ||
=====================================

2's complement:
-----------------
Add 1 to above result
10011100 + 1 = 10011101
=====================================
||    2's complement: 10011101    ||
=====================================