Question

convert -97 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

This is negative. so, follow these steps to convert this to various binary formats.
Divide 97 successively by 2 until the quotient is 0
   > 97/2 = 48, remainder is 1
   > 48/2 = 24, remainder is 0
   > 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 1100001
So, 97 of decimal is 1100001 in binary
Adding 1 zeros on left hand side of this number to make this of length 8
So, 97 in normal binary format is 01100001
sign-magnitude:
-----------------
set 1 as left most bit, since this number is negative.
so, 01100001 becomes 11100001
=====================================
||    sign-magnitude: 11100001    ||
=====================================

1's complement:
-----------------
flip all the bits. Flip all 0's to 1 and all 1's to 0.
   01100001 is flipped to 10011110
=====================================
||    1's complement: 10011110    ||
=====================================

2's complement:
-----------------
Add 1 to above result
10011110 + 1 = 10011111
=====================================
||    2's complement: 10011111    ||
=====================================

for excess-127:
---------------
for binary value add 127 to -97
127-97 = 30
Divide 30 successively by 2 until the quotient is 0
   > 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 11110
So, 30 of decimal is 11110 in binary
=================================
||    excess-127: 00011110    ||
=================================