Question

• i.Show that 0.010011₂ is the binary representation of 0.296875₁₀
• ii.A computer system allows only 4 binary digits after the decimal point. Write the two binary values with exactly 4 digits after the decimal point that ‘sandwich’ 0.010011₂.

• iii.Using the two binary ‘sandwich’ values that you found in (ii), write down the minimum and maximum binary values that sandwich the result of 0.010011₂ + 0.010011₂

• iv.Convert each of the binary values you found in (iii) to decimal notation. Give the minimum and maximum values in decimal notation.
• v.Calculate, in decimal, the value of 0.296875₁₀ + 0.296875₁₀ (Your answer is the actual value so it should not be rounded). By what percentage, rounded to the nearest whole percent, does the maximum value exceed the actual value? Your answer should show the actual value, the percentage and your workings for full marks.

Answer 1

Here, I am providing my handwritten solutions of above questions:

In case you have doubt like how we are finding just smaller and just greater value then i would like to answer that we are just changing bits in such a way that we get the corresponding smaller and greater value.