Question

Convert -122 to 8-bit sign magnitude, 1's complement and 2's complement

Answer 1

-122
-------
This is negative. so, follow these steps to convert this to various binary formats.
Divide 122 successively by 2 until the quotient is 0
122/2 = 61, remainder is 0
61/2 = 30, remainder is 1
30/2 = 15, remainder 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 1111010
Adding 1 zeros on left hand side of this number to make this of length 8
So, 122 in normal binary format is 01111010
sign-magnitude:
-----------------
set 1 as left most bit, since this number is negative.
so, 01111010 becomes 11111010
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||    sign-magnitude: 11111010    ||
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1's complement:
-----------------
flip all the bits. Flip all 0's to 1 and all 1's to 0.
   01111010 is flipped to 10000101
=====================================
||    1's complement: 10000101    ||
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2's complement:
-----------------
Add 1 to above result
10000101 + 1 = 10000110
=====================================
||    2's complement: 10000110    ||
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