Question

convert -44 to 8-bit sign-magnitude, 1's complement, 2's complement and excess-127.

Please be careful and explain all the steps and details.

Answer 1

-44
------
This is negative. so, follow these steps to convert this to various binary formats.
Divide 44 successively by 2 until the quotient is 0
   > 44/2 = 22, remainder is 0
   > 22/2 = 11, remainder is 0
   > 11/2 = 5, remainder is 1
   > 5/2 = 2, remainder is 1
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 101100
So, 44 of decimal is 101100 in binary
Adding 2 zeros on left hand side of this number to make this of length 8
So, 44 in normal binary format is 00101100
sign-magnitude:
-----------------
set 1 as left most bit, since this number is negative.
so, 00101100 becomes 10101100
=====================================
||    sign-magnitude: 10101100    ||
=====================================

1's complement:
-----------------
flip all the bits. Flip all 0's to 1 and all 1's to 0.
   00101100 is flipped to 11010011
=====================================
||    1's complement: 11010011    ||
=====================================

2's complement:
-----------------
Add 1 to above result
11010011 + 1 = 11010100
=====================================
||    2's complement: 11010100    ||
=====================================
for excess-127:
---------------
for binary value add 127 to -44
127-44 = 83
Divide 83 successively by 2 until the quotient is 0
   > 83/2 = 41, remainder is 1
   > 41/2 = 20, remainder is 1
   > 20/2 = 10, remainder is 0
   > 10/2 = 5, remainder is 0
   > 5/2 = 2, remainder is 1
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1010011
So, 83 of decimal is 1010011 in binary
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||    excess-127: 01010011    ||
=================================