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Let

a = 1.0 x 2⁹

b = -1.0 x 2⁹

c = 1.0 x 2¹

A. Convert these floating point numbers to binary using the simple model described in the textbook for representing (express the result in binary) :

14-bits

5 bits for the exponent with a bias of 15

8 bits for the normalized mantissa (no hidden bit)

1 bit for the sign

a = __________________

b = __________________

c = __________________

B. Perform the following calculations using binary arithmetic:

b + (a + c) = ________________

(b + a) + c = ________________

C. Explain why you got the result you did.

D. Would you get the same kind of result using multiplication rather then addition (why or why not)?

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