Question

In: Computer Science

1-List the different ways to represent signed integers and represent (-75) in these ways. Convert the...

1-List the different ways to represent signed integers and represent (-75) in these ways.

Convert the following:

  1. (345)10 = (                          )2      
  2. (563)10 = (                            )16
  3. (2AB5)16 = (                           )2
  4. (1011111100111100)2 = (                        )16

Find the two's complement for the following

  1. (11011101100100)2
  2. (34BC)16

           

2- Compute the following signed integer and determine if either there carry or overflow

  1. (01001110)2 + (10101100)2
  1. (01111000)2+ (00110001)2
  1. (00101101)2 - (01111110)2

Solutions

Expert Solution

=====================================

Different ways to represent signed integers are-------

1. sign and magnitude

2. 1's complement

3. 2's complement

Now represent   -75 In these ways

1. sign and magnitude

so we use 7 bit to represent 75 and 1 bit for sign

(-75)10 = (11001011)2      

2. 1's complement

   -75 =         10110100

3. 2's complement

      -75 = 10110101

====================================

Convert the following

A. (345)10 = (     )2

   345/2 = 172 + 1
   172/2 = 86   + 0
   86/2 = 43   + 0
   43/2 = 21   + 1
   21/2 = 10   + 1
   10/2 = 5    + 0
   5/2   = 2    + 1
   2/2   = 1    + 0
   1/2   = 0    + 1

   (345)10 = (101011001)2
  
B. (563)10 = ( )16

   563/16 = 35 + 3
   35/16   = 2 + 3
   2/16    = 0 + 2
  
   (563)10 = (233)16
  

C. (2AB5)16 = (   )2

   2      A       B      5
      0010 1010 1011 0101

    (2AB5)16 = (10101010110101)2


D. (1011111100111100)2 = (    )16

       1011 1111 0011 1100
         B     F    3   C
       
     (1011111100111100)2 = (BF3C)16
     ===========================================================================

Two's complement for the following
   
A. (11011101100100)2
     invert the digit and add 1 to it
     step 1 -Invert the digit
            11011101100100
           00100010011011
      step2 - add 1 to the final result
             00100010011011
                    + 1
             00100010011100     
            
      so now two's complement of (11011101100100)2 is 00100010011100     
    
B. (34BC)16

To find a twos complement of hexadecimal first we have to convert it into its binary form

        3         4       B       C
     0011 0100 1011   1100
   
      invert the digit and add 1 to it
     step 1 -Invert the digit
            0011 0100 1011 1100
           1100 1011 0100 0011
      step2 - add 1 to the final result
             1100101101000011
                    + 1
             1100101101000100
            
      so now two's complement of (0011010010111100)2 is 1100101101000100
    
      1100   1011   0100 0100  
       C          B    4 4
     
       So two's complement of (34BC)16 = (CB44)16
     

======================================================================================    
2 compute
A. (01001110)2 + (10101100)2 = (    )2


   + 1 0 0 1 1 1 0    (+ 78)
   - 0 1 0 1 1 0 0               (- 44)
     ---------------------------------
   + 0 1 0 0 0 1 0              (+ 34)
  
   (01001110)2 + (10101100)2 = (00100010)2


********************************************************************    


B. (01111000)2+ (00110001)2 = (   )2

          0 1 1 1 1 0 0 0    ( 120)
      + 0 0 1 1 0 0 0 1           (49)
      ===================
        1 0 1 0 1 0 0 1    (169)
      
      
        (01111000)2+ (00110001)2 = (010101001)2

**********************************************************************
      
C. (00101101)2 - (01111110)2   = ( )2
          45     -   126
    
      first complement of 1111110 is 0000001
    
      hence minud =                    0101101
      first complement of subtrahend = 0000001
                                       0101110
                                      --------
                                       1010001
                                     
      no carry hence the difference is negative
         answer is   -1010001        (-81)
    
    
  

     
   

venereology answered 6 months ago
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