Question

In: Computer Science

convert -97 to 8-bit sign-magnitude, 1's complement, 2's complement and excess-127. Please be careful and explain...

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.

Solutions

Expert Solution

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    ||
=================================

Related Solutions

convert -44 to 8-bit sign-magnitude, 1's complement, 2's complement and excess-127. Please be careful and explain...
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.
convert -44 to 8-bit sign-magnitude, 1's complement, 2's complement and excess-127. Please be careful and explain...
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.
convert -44 to 8-bit sign-magnitude, 1's complement, 2's complement and excess-127. Please be careful and explain...
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.
Convert -18 to 8-bit sign magnitude, 1's complement and 2's complement.
Convert -18 to 8-bit sign magnitude, 1's complement and 2's complement.
Convert -18 to 8-bit sign magnitude, 1's complement and 2's complement.
Convert -18 to 8-bit sign magnitude, 1's complement and 2's complement.
Convert -18 to 8-bit sign magnitude, 1's complement and 2's complement.
Convert -18 to 8-bit sign magnitude, 1's complement and 2's complement.
Convert -122 to 8-bit sign magnitude, 1's complement and 2's complement
Convert -122 to 8-bit sign magnitude, 1's complement and 2's complement
Convert -122 to 8-bit sign magnitude, 1's complement and 2's complement
Convert -122 to 8-bit sign magnitude, 1's complement and 2's complement
Convert -122 to 8-bit sign magnitude, 1's complement and 2's complement
Convert -122 to 8-bit sign magnitude, 1's complement and 2's complement
Show the decimal integer 79 in 8-bit sign magnitude, one's complement, two's complement and excess-127 respectively...
Show the decimal integer 79 in 8-bit sign magnitude, one's complement, two's complement and excess-127 respectively in the given order, separated by comma.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT