Problem Set Answers: Data Representation

 

    1. 33110 = 01 0100 1011
    2. -11210 = 11 1001 0000
    3. 20610 = 00 1100 1110
    1.      10 1101 1100  -
   + 11 0110 0011  -
   --------------
     10 0011 1111  -

    2.      00 0101 1011  +
   + 11 0101 1001  -
   --------------
     11 1011 0100  -

    3.      01 0110 0101  +
   + 01 0111 0100  +
   --------------
     10 1101 1001  -   overflow

    1.      00 04 02 84   +
   + 39 43 A1 9C   +
   --------------
     39 47 A4 20   +

    2.      00 03 5E 99   +
   + FF FA 27 38   -
   --------------
     FF FD 85 D1   -

    3.      FF FD 3A 09   -
   + 00 05 C9 14   +
   --------------
     00 03 03 1D   +
    1. 147.7812510 = 10010011.110012
    2. 91.448310 = 1011011.01112 (the next two bits are 0's so I left them off)
    3. 232.089710 = 11101000.0001012
    4. 29.20710 = 11101.0011012 
    1. 18.125 = 1.0010001 x 24
(4 + 127)10 = 13110 = 100000112
sign: 0
exp: 1000 0011
signif: 001 0001 0000 0000 0000 0000
IEEE rep: 0 1000 0011 001 0001 0000 0000 0000 0000

    2. 194.03125 = 1.100001000001 x 27
(7 + 127)10 = 13410 = 100001102
sign: 0
exp: 1000 0110
signif: 100 0010 0000 1000 0000 0000
IEEE rep: 0 1000 0110 100 0010 0000 1000 0000 0000

    3. - 0.23392 = - 1.11011111 x 2-3
(-3 + 127)10 = 12410 = 011111002
sign: 1
exp: 0111 1100
signif: 110 1111 1000 0000 0000 0000
IEEE rep: 1 0111 1100 110 1111 1000 0000 0000 0000

    4. - 3144.56 = - 1.100010010001000111101 x 211
(11 + 127)10 = 13810 = 100010102
sign: 1
exp: 1000 1010
signif: 100 0100 1000 1000 1111 0100
IEEE rep: 1 1000 1010 100 0100 1000 1000 1111 0100

    5. 9,060,100 = 1.000101000111111000001 x 223
(23 + 127)10 = 15010 = 101010102
sign: 0
exp: 1010 1010
signif: 000 1010 0011 1111 0000 0100
IEEE rep: 0 1010 1010 000 1010 0011 1111 0000 0100

    6. 0.0031 = 1.1001011 x 2-9
(-9 + 127)10 = 11810 = 011101102
sign: 0
exp: 0111 0110
signif: 100 1011 0000 0000 0000 0000
IEEE rep: 0 0111 0110 100 1011 0000 0000 0000 0000

    1.      1.1 * 2-3 = .00112
               = (1/8 + 1/16)10
               = .187510

    2.      - 1.11 * 233 = - (1 * 233 + 1 * 232 + 1 * 231)10
                 = - (8,589,934,592 + 4,294,967,296 + 2,147,483,648)10
                 = - 15,032,385,53610

    3.      1.0011 * 2-10 = .000000000100112
                  = (1/1024 + 1/8192 + 1/16384)10
                  = .0011596710

    4.      1.010011 * 2-4 = .00010100112
                   = (1/16 + 1/64 + 1/512 + 1/1024)10
                   = .08105469

    5.      1.011 0010 1 * 26 = 1011001.012
                   = 64 + 16 + 8 + 1 + .2510
                   = 89.25

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