April 2000
LD201 : LOGIC DESIGN

QUESTION 2

Total Marks: 15 Marks

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for Question 2

This question concerns a 16-bit floating-point format, with an 11-bit mantissa in two’s-complement format and a 5-bit exponents in sign-modulus format.

(a) What are the largest and smallest positive and negative values that can be represented normalized in this format? [4 marks]

(b) Express the numbers –0.1238 and 4.5678 in normal form in this format.. [4 marks]

(c) Hence add these two values, and express the result as a decimal fraction. [4 marks]

(d) The IEEE 754 standard for floating point reserves some bit patterns for representing certain special values, apart from the patterns used to represent ‘normal’ values. Explain how each of the following special values might arise in floating point arithmetic:

(i) positive infinity;

(ii) negative infinity;

(iii) ‘not a number’.

[3 marks]