CS 2734 Computer Organization II

• From Tanenbaum text:
  • 0.5 = 0.1 = 1.0 x 2^{-1} in normalized form
    sign is 0
    exponent in excess 127 is 126 or 01111110
    mantissa is 0
    IEEE single precision is x3F000000
    
  • 1.0 = 1.0 x 2^{0} in normalized form
    sign is 0
    exponent in excess 127 is 127 or 01111111
    mantissa is 0
    IEEE single precision is x3F800000
    
  • 1.5 = 1.1 x 2^{0} in normalized form
    sign is 0
    exponent in excess 127 is 127 or 01111111
    mantissa is 10000000000000000000000
    IEEE single precision is x3FC00000
    
• Tanenbaum page 572 number 1
  • 9 = 1001 = 1.001 x 2^{3} in normalized form
    sign is 0
    exponent in excess 127 is 130 or 10000010
    mantissa is 00100000000000000000000
    IEEE single precision is x41100000
    
  • 5/32 = 5 x 2^{-5} = 1.01 x 2^{-3} in normalized form
    sign is 0
    exponent in excess 127 is 124 or 01111100
    mantissa is 01000000000000000000000
    IEEE single precision is x3E200000
    
  • -5/32 same as previous except sign bit is 1.
    IEEE single precision is xBE200000
    
  • 6.125 = 6 x 2^0 + 1 x 2^{-3} = 1.10001 x 2^{2}
    sign is 0
    exponent in excess 127 is 129 or 10000001
    mantissa is 100010000000000000000000
    IEEE single precision is x40C40000
    
• Tanenbaum page 573 number 2
  • x42E48000 = 0100 0010 1110 0100 1000 0000 0000 0000
    sign bit is 0
    exponent is 10000101 = 133, converting = 6
    mantissa is 1.11001001
    unnormalizing we have 1.11001001 x 2^6 or 1110010.01 = 114.25
    
  • This is an extra problem I did by mistake
    x42348000 = 0100 0010 0011 0100 1000 0000 0000 0000
    sign bit is 0
    exponent is 10000100 = 132, converting = 5
    mantissa is 1.01101001
    unnormalizing we have 1.01101001 x 2^5 or 101101.001 = 45.125
    
  • x3F880000 = 0011 1111 1000 1000 0000 0000 0000 0000
    sign bit is 0
    exponent is 011111111 = 127, converting = 0
    mantissa is 1.0001
    unnormalizing we have 1.0001 = 1 + 2^{-4} = 1.0625
    
  • x00800000 = 0000 0000 1000 0000 0000 0000 0000 0000
    sign bit is 0
    exponent is 00000001 = 1, converting is -126
    manissa is 1.0
    unnormalizing we have 1.0 x 2^{-126} = 1.17549 x 10^{-38}.
  • xC7F00000 = 1100 0111 1111 0000 0000 0000 0000 0000
    sign bit is 1 so overall number is negative
    exponent is 10001111 = 128 + 15 = 143, converting is 16
    mantissa is 1.111
    unnormalizing we have 1.111 x 2^{16} = 1111 x 2^{13} = 15 x 8192 = 122,880