Question

Using the three-bit exponent field and four-bit significand, what is the bit pattern for the -2.5? (show work)

Answer 1

11000100

Explanation:
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-2.5
Converting 2.5 to binary
   Convert decimal part first, then the fractional part
   > First convert 2 to binary
   Divide 2 successively by 2 until the quotient is 0
      > 2/2 = 1, remainder is 0
      > 1/2 = 0, remainder is 1
   Read remainders from the bottom to top as 10
   So, 2 of decimal is 10 in binary
   > Now, Convert 0.50000000 to binary
      > Multiply 0.50000000 with 2.  Since 1.00000000 is >= 1. then add 1 to result
      > This is equal to 1, so, stop calculating
   0.5 of decimal is .1 in binary
   so, 2.5 in binary is 00000010.1
-2.5 in simple binary => 10.1
so, -2.5 in normal binary is 10.1 => 1.01 * 2^1

8-bit format:
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sign bit is 1(-ve)
exponent bits are (3+1=4) => 100
   Divide 4 successively by 2 until the quotient 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 100
   So, 4 of decimal is 100 in binary
frac/significant bits are 0100

so, -2.5 in 8-bit format is 1 100 0100