Question

Assume that you have a 12-bit floating point number system, similar to the IEEE floating point standard, with the format shown below and a bias of 7. The value of a floating point number in this system is represented as   

FP = (-1)^S X 1.F X 2^(E-bias)

for the floating point numbers A = 8.75 and B = -5.375. The binary representation of A is given as

A = 0101 0000 1100

Show the hexidecimal representation of B.

Answer 1

0xCAC

Explanation:
-------------
-5.375
Converting 5.375 to binary
   Convert decimal part first, then the fractional part
   > First convert 5 to binary
   Divide 5 successively by 2 until the quotient is 0
      > 5/2 = 2, remainder is 1
      > 2/2 = 1, remainder is 0
      > 1/2 = 0, remainder is 1
   Read remainders from the bottom to top as 101
   So, 5 of decimal is 101 in binary
   > Now, Convert 0.37500000 to binary
      > Multiply 0.37500000 with 2.  Since 0.75000000 is < 1. then add 0 to result
      > Multiply 0.75000000 with 2.  Since 1.50000000 is >= 1. then add 1 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
   0.375 of decimal is .011 in binary
   so, 5.375 in binary is 00000101.011
-5.375 in simple binary => 101.011
so, -5.375 in normal binary is 101.011 => 1.01011 * 2^2

12-bit format:
--------------------
sign bit is 1(-ve)
exponent bits are (7+2=9) => 1001
   Divide 9 successively by 2 until the quotient is 0
      > 9/2 = 4, remainder is 1
      > 4/2 = 2, remainder is 0
      > 2/2 = 1, remainder is 0
      > 1/2 = 0, remainder is 1
   Read remainders from the bottom to top as 1001
   So, 9 of decimal is 1001 in binary
frac/significant bits are 0101100

so, -5.375 in 12-bit format is 1 1001 0101100
Hexadecimal     Binary
    0           0000
    1           0001
    2           0010
    3           0011
    4           0100
    5           0101
    6           0110
    7           0111
    8           1000
    9           1001
    A           1010
    B           1011
    C           1100
    D           1101
    E           1110
    F           1111
Use this table to convert from binary to hexadecimal
Converting 110010101100 to hexadecimal
1100 => C
1010 => A
1100 => C
So, in hexadecimal 110010101100 is 0xCAC

in hexadecimal it is 0xCAC