Question

In representing -1/4 in IEEE 754, the value of the exponent plus bias (127) is

11111101

01111101

10000000

01111111

Answer 1

b)  01111101

Explanation:
-------------
-0.25
Converting 0.25 to binary
   Convert decimal part first, then the fractional part
   > First convert 0 to binary
   Divide 0 successively by 2 until the quotient is 0
   Read remainders from the bottom to top as
   So, 0 of decimal is  in binary
   > Now, Convert 0.25000000 to binary
      > Multiply 0.25000000 with 2.  Since 0.50000000 is < 1. then add 0 to result
      > Multiply 0.50000000 with 2.  Since 1.00000000 is >= 1. then add 1 to result
      > This is equal to 1, so, stop calculating
   0.25 of decimal is .01 in binary
   so, 0.25 in binary is 00000000.01
-0.25 in simple binary => .01
so, -0.25 in normal binary is .01 => 1. * 2^-2

single precision:
--------------------
sign bit is 1(-ve)
exponent bits are (127-2=125) => 01111101
   Divide 125 successively by 2 until the quotient is 0
      > 125/2 = 62, remainder is 1
      > 62/2 = 31, remainder is 0
      > 31/2 = 15, remainder is 1
      > 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 1111101
   So, 125 of decimal is 1111101 in binary
so, 8-bit exponent is 01111101