December 1999
LD201 : LOGIC DESIGN

QUESTION 2

Total Marks: 15 Marks

• Question 1
• Question 3
• Question 4
• Question 5
• Cover Page

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SUGGESTED SOLUTIONS
for Question 2

This question concerns a 9-bit floating point format, consisting of a 5-bit mantissa and a 4-bit exponent, both in two’s-complement format.

Give in decimal the largest and smallest positive and negative values that can be represented in this format in normalized form.

Perform the following conversions:

(i) the sign-modulus integer represented by 10001 into this floating-point format, normalized;

(ii) the one’s-complement integer represented by 10001 into this floating-point format, normalized;

(iii) the number represented in this floating-point format by 1 0001 0 001 into decimal.

To add floating-point numbers, one must usually rescale to match exponents, before adding the mantissas and renormalizing the result.

(i) Rescale the two numbers with smaller exponents from part (b) to match the number with largest exponent. [2 marks]

(ii) Add the three mantissas. (Hint: add any two, then add the third to the sum.) [1 mark]

(iii) What can you say about the result of adding the three mantissas? [2 marks]

What can you do to rectify the problem identified above, without changing the floating-point format?