8 ry using the 8bit signed2scomplement representation Then p

8. ry, using the 8-bit signed-2\'s-complement representation. Then perform the binary equivalent of (-106)+(-72). Convert to decimal and verify that it is correct or explain why it is not. the answer back (5 points) Convert 110011100011110000101011101011 to hexadecimal

Solution

8. +75
   So we will write binary for 75 i.e 01001011 and thats it because in 2\'complememt for positive numbers we just need their binary.
   Similarly for +53 we will have 0011 0101

   -106 + (-72)

   -106 - first we will write binary of 106 , we will do 1\'s complement and then add 1
      so 106 = 0110 1010
               1001 0101 (1\'s complement)
               1001 0101
               +       1
              ---------------
               10010110
     Similarly for -72 we have:
               0100 1000
               1011 0111 (1\'s complement)
               +       1
              -------------
               1011 1000

Solving -106 + (-72) = 01001110 (in binary) (1 bit is overflowing). If we convert this to decimal we get 78 and not -178
If we solve -106 -72 we get -178
If we look at the 2\'s complement of -178 it is
      1011 0010 (Binary)
      0100 1101 (1\'s complement)
      +       1
    ------------
      01001110 --> This matches with our answer.
         

Convert 11 0011 1000 1111 0000 1010 1110 1011 to hexadecimal

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