Question

Convert the decimal floating point value 8.125 to a 12 bit binary floating point value. Use a sign bit, 3 bits (excess 3) for the exponent and an 8 bit significand. Enter just a 12 digit binary value ( e.g. 0 000 11110000 ) spaces ignored.

Answer 1

Converting 8.125 to binary
   Convert decimal part first, then the fractional part
   > First convert 8 to binary
   Divide 8 successively by 2 until the quotient is 0
      > 8/2 = 4, remainder is 0
      > 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 1000
   So, 8 of decimal is 1000 in binary
   > Now, Convert 0.125 to binary
      > Multiply 0.125 with 2.   Since 0.25 is < 1. then add 0 to result
      > Multiply 0.25 with 2.    Since 0.5 is < 1. then add 0 to result
      > Multiply 0.5 with 2.     Since 1.0 is >= 1. then add 1 to result
      > This is equal to 1, so, stop calculating
   0.125 of decimal is .001 in binary
   so, 8.125 in binary is 1000.001
8.125 in simple binary => 1000.001
so, 8.125 in normal binary is 1000.001 => 1.000001 * 2^3

12-bit format:
----------------
sign bit is 0(+ve)
exp bits are (3+3=6) => 110
frac bits are 00000100

so, 8.125 in 12-bit format format is 0 110 00000100
Answer: 0 110 00000100