Question

1. (5 pts) Assuming three-bit exponent field and four-bit significand, what is the bit pattern for 11.25(show work)

Answer 1

01100110

Explanation:
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11.25
Converting 11.25 to binary
   Convert decimal part first, then the fractional part
   > First convert 11 to binary
   Divide 11 successively by 2 until the quotient is 0
      > 11/2 = 5, remainder is 1
      > 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 1011
   So, 11 of decimal is 1011 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, 11.25 in binary is 00001011.01
11.25 in simple binary => 1011.01
so, 11.25 in normal binary is 1011.01 => 1.011 * 2^3

8-bit format:
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sign bit is 0(+ve)
exponent bits are (3+3=6) => 110
   Divide 6 successively by 2 until the quotient is 0
      > 6/2 = 3, remainder is 0
      > 3/2 = 1, remainder is 1
      > 1/2 = 0, remainder is 1
   Read remainders from the bottom to top as 110
   So, 6 of decimal is 110 in binary
frac/significant bits are 0110

so, 11.25 in 8-bit format is 0 110 0110