Question

1. Assuming three-bit exponent field and four-bit significand, what is the bit pattern for -8.75?

Answer 1

11100001

Explanation:
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-8.75
Converting 8.75 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 0.75000000 to binary
      > 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
   0.75 of decimal is .11 in binary
   so, 8.75 in binary is 00001000.11
-8.75 in simple binary => 1000.11
so, -8.75 in normal binary is 1000.11 => 1.0001 * 2^3

8-bit format:
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sign bit is 1(-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 0001

so, -8.75 in 8-bit format is 1 110 0001