Question

Store -2.5 as tiny floating point based on 8-bit floating point presentation. show your working

Show bias

Exponent

Fill in bits

Final 1 bye presentation

INTRODUCTION TO COMPUTER SYSTEMS

SHOW YOUR WORKING

Answer 1

Answer:
--------
Show bias Exponent: 8
Final 1 bye presentation:   11000010

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:
--------------------
sign bit is 1(-ve)
exponent bits are (7+1=8) => 1000
   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
frac/significant bits are 010

so, -2.5 in 8-bit format is 1 1000 010