Store -2.75 in Tiny Floating Point form.

Expert Solution

11000011

Explanation:
-------------
Tiny Floating Point form is of 8 bits.
1 sign bit, 4 exponent bits, 3 mantissa bits.

-2.75
Converting 2.75 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 0.75000000 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, 2.75 in binary is 00000010.11
-2.75 in simple binary => 10.11
so, -2.75 in normal binary is 10.11 => 1.011 * 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 011

so, -2.75 in 8-bit format is 1 1000 011

venereology answered 2 years ago

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