Question

Assuming three-bit exponent field and four-bit significant, what is the bit pattern for 5.75

Answer 1

01010111

Explanation:
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5.75
Converting 5.75 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 0.75000000 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, 5.75 in binary is 00000101.11
5.75 in simple binary => 101.11
so, 5.75 in normal binary is 101.11 => 1.0111 * 2^2

8-bit format:
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sign bit is 0(+ve)
exponent bits are (3+2=5) => 101
   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
frac/significant bits are 0111

so, 5.75 in 8-bit format is 0 101 0111